, Roberto Stok [aut],
Bank of Italy [cph]| Title: | Time Series and Econometric Modeling |
|---|---|
| Description: | Time series analysis, (dis)aggregation and manipulation, e.g. time series extension, merge, projection, lag, lead, delta, moving and cumulative average and product, selection by index, date and year-period, conversion to daily, monthly, quarterly, (semi)annually. Simultaneous equation models definition, estimation, simulation and forecasting with coefficient restrictions, error autocorrelation, exogenization, add-factors, impact and interim multipliers analysis, conditional equation evaluation, rational expectations, endogenous targeting and model renormalization, structural stability, stochastic simulation and forecast, optimal control. |
| Authors: | Andrea Luciani [aut, cre]
, Roberto Stok [aut],
Bank of Italy [cph] |
| Maintainer: | Andrea Luciani <[email protected]> |
| License: | GPL-3 |
| Version: | 4.0.3 |
| Built: | 2024-11-25 19:30:05 UTC |
| Source: | CRAN |
BIMETS is a software framework developed by using R language and designed for time series analysis and econometric modeling, which allows creating and manipulating time series, specifying simultaneous equation models of any size by using a kind of high-level description language, and performing model estimation and structural stability analysis, deterministic and stochastic simulation and forecasting, also on rational expectations model, and optimal control.
Besides, BIMETS computational capabilities provide many tools to pre-process data and post-process results, designed for statisticians and economists. These operations are fully integrated with the R environment.
The package can be installed and loaded in R with the following commands (with R> as the R command prompt):
R> install.packages('bimets')
R> library(bimets)
If you have general questions about using BIMETS, or for bug reports, please use the git issue tracker or write to the maintainer.
| TIME SERIES |
BIMETS supports daily, weekly, monthly, quarterly, semiannual and yearly time series. Time series with a frequency of 24 and 36 periods per year are also supported. Time series are created by the TIMESERIES function.
Example:
R> #yearly time series
R> myTS <- TIMESERIES(1:10,START=as.Date('2000-01-01'),FREQ=1)
R> #monthly time series
R> myTS <- TIMESERIES(1:10,START=c(2002,3),FREQ='M')
The main BIMETS time series capabilities are:
- Indexing
- Aggregation / Disaggregation
- Manipulation
| Time Series Indexing |
The BIMETS package extends R indexing capabilities in order to ease time series analysis and manipulation. Users can access and modify time series data:
- by year-period: users can select and modify observations by providing the requested years and periods, i.e. ts[[year,period]], ts[[start]] and ts[[start,end]], given start <- c(year1,period1); end <- c(year2,period2);
- by date: users can select and modify a single observation by date by using the syntax ts['Date'], or multiple observations by using ts['StartDate/EndDate'];
- by observation index: users can select and modify observations by simply providing the array of requested indices, i.e. ts[indices];
Example:
R> #create a daily time series
R> myTS <- TIMESERIES((1:100),START=c(2000,1),FREQ='D')
R> myTS[1:3] #get first three obs.
R> myTS[[2000,14]] #get year 2000 period 14
R> start <- c(2000,20)
R> end <- c(2000,30)
R> myTS[[start]] #get year 2000 period 20
R> myTS[[start,end]] #get from year-period 2000-20 to 2000-30
R> myTS['2000-01-12'] #get Jan 12, 2000 data
R> myTS['2000-02-03/2000-02-14'] #get Feb 3 up to Feb 14
R> myTS['2000-01-15'] <- NA #assign to Jan 15, 2000
R> myTS[[2000,42]] <- NA #assign to Feb 11, 2000
R> myTS[[2000,100]] <- c(-1,-2,-3) #extend time series starting from period 100
R> myTS[[start]] <- NA #assign to year-period 2000-20
R> myTS[[start,end]] <- 3.14 #assign from year-period 2000-20 to 2000-30
R> myTS[[start,end]] <- -(1:11) #assign multiple values
#from year-period 2000-20 to 2000-30
| Time Series Aggregation / Disaggregation |
The BIMETS package provides advanced (dis)aggregation capabilities, having linear interpolation capabilities in disaggregation, and several aggregation functions (e.g. STOCK, SUM, AVE, etc.) while reducing the time series frequency.
Example:
R> #create a monthly time series R> myMonthlyTS <- TIMESERIES(1:100,START=c(2000,1),FREQ='M') R> #convert to yearly time series by using the average as aggregation fun R> myYearlyTS <- YEARLY(myMonthlyTS,'AVE') R> #convert to daily by using central interpolation as disaggregation fun R> myDailyTS <- DAILY(myMonthlyTS,'INTERP_CENTER')
| Time Series Manipulation |
The BIMETS package provides, among others, the following time series manipulation capabilities:
- Time series extension TSEXTEND
- Time series merging TSMERGE
- Time series projection TSPROJECT
- Lag TSLAG
- Lead TSLEAD
- Lag differences: standard, percentage, and logarithmic TSDELTA TSDELTAP TSDELTALOG
- Cumulative product CUMPROD
- Cumulative sum CUMSUM
- Moving average MOVAVG
- Moving sum MOVSUM
- Time series data presentation TABIT
Example:
R> #define two time series
R> myTS1 <- TIMESERIES(1:100,START=c(2000,1),FREQ='M')
R> myTS2 <- TIMESERIES(-(1:100),START=c(2005,1),FREQ='M')
R> #extend time series up to Apr 2020 with quadratic formula
R> myExtendedTS <- TSEXTEND(myTS1,UPTO=c(2020,4),EXTMODE='QUADRATIC')
R> #merge two time series with sum
R> myMergedTS <- TSMERGE(myExtendedTS,myTS2,fun='SUM')
R> #project time series on arbitrary time range
R> myProjectedTS <- TSPROJECT(myMergedTS,TSRANGE=c(2004,2,2006,4))
R> #lag and delta% time series
R> myLagTS <- TSLAG(myProjectedTS,2)
R> myDeltaPTS <- TSDELTAP(myLagTS,2)
R> #moving average
R> myMovAveTS <- MOVAVG(myDeltaPTS,5)
R> #print data
R> TABIT(myMovAveTS,
myTS1,
TSRANGE=c(2004,8,2004,12)
)
Date, Prd., myMovAveTS , myTS1
Aug 2004, 8 , , 56
Sep 2004, 9 , , 57
Oct 2004, 10 , 3.849002 , 58
Nov 2004, 11 , 3.776275 , 59
Dec 2004, 12 , 3.706247 , 60
| ECONOMETRIC MODELING |
BIMETS econometric modeling capabilities comprehend:
- Model Description Language
- Estimation
- Structural Stability
- Simulation
- Rational Expectations
- Stochastic Simulation
- Multipliers Analysis
- Endogenous Targeting
- Optimal Control
We will go through each item of the list with a simple Klein model example (ref: "Economic Fluctuations in the United States 1921-1941" by L. R. Klein, Wiley and Sons Inc., New York, 1950).
For more realistic scenarios, several advanced econometric exercises on the US Federal Reserve FRB/US econometric model (e.g., dynamic simulation in a monetary policy shock, rational expectations, endogenous targeting, stochastic simulation, etc.) are available in the "US Federal Reserve quarterly model (FRB/US) in R with bimets" vignette.
| Model Description Language |
BIMETS provides a language to specify an econometric model unambiguously. This section describes how to create a model and its general structure. The specification of an econometric model is translated and identified by keyword statements which are grouped in a model file, i.e. a plain text file or a character variable with a specific syntax. Collectively, these keyword statements constitute the BIMETS Model Description Language (from now on MDL). The model specifications consist of groups of statements. Each statement begins with a keyword. The keyword classifies the component of the model which is being specified.
Below is an example of Klein's model, which can either be stored in an R variable of class character or in a plain text file with an MDL compliant syntax.
The content of the klein1.txt variable is:
R> klein1.txt <- " MODEL COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1921 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END "
Given:
- cn as Private Consumption Expenditure;
- i as Investment;
- w1 as Wage Bill of the Private Sector (Demand for Labor);
- p as Profits;
- k as Stock of Capital Goods;
- y as Gross National Product;
- w2 as Wage Bill of the Government Sector;
- time as an annual index of the passage of time;
- g as Government Expenditure plus Net Exports;
- t as Business Taxes. a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4 are coefficients to be estimated.
This system has only six equations, three of which must be fitted to assess the coefficients. It may not seem challenging to solve this system. However, the objective complexity emerges if you look at the incidence graph in the following figure, wherein endogenous variables are plotted in blue and exogenous variables are plotted in pink.
Each edge states a simultaneous dependence from a variable to another, e.g. the w1 equation depends on the current value of the time time series; complexity arises because in this model there are several circular dependencies, one of which is plotted in dark blue.
A circular dependency in the incidence graph of a model implies that the model is a simultaneous equations model. It must be estimated using ad-hoc procedures; moreover, it can be simulated, e.g. performing a forecast, only using an iterative algorithm.
As shown in the code, the model definition is quite intuitive. The first keyword is MODEL, while at the end of the model definition we can find the END keyword. Available tags in the definition of a generic BIMETS model are:
- EQUATION> or BEHAVIORAL> indicate the beginning of a series of keyword statements describing a behavioral equation;
- IDENTITY> indicates the beginning of a series of keyword statements describing an identity or technical equation;
- EQ> specifies the mathematical expression for a behavioral equation or an identity equation;
- COEFF> specifies the coefficient names used in the EQ> keyword statement of a behavioral equation;
- ERROR> specifies an autoregressive process of a given order for the regression error;
- PDL> defines an Almon polynomial distributed lag;
- RESTRICT> is a keyword that can be used to specify linear coefficient restrictions;
- IF> is used to conditionally evaluate an identity during a simulation, depending on a logical expression's value. Thus, it is possible to have a model alternating between two or more identity specifications for each simulation period, depending upon results from other equations;
- IV> specifies the mathematical expression for an instrumental variable used in a behavioral equation;
- COMMENT> can be used to insert comments into a model;
The mathematical expression in the EQ> and IF> definitions can include the standard arithmetic operators, parentheses, and the following MDL time series functions:
- TSLAG(ts,i): lag the ts time series by i-periods;
- TSLEAD(ts,i): lead the ts time series by i-periods;
- TSDELTA(ts,i): i-periods difference of the ts time series;
- TSDELTAP(ts,i): i-periods percentage difference of the ts time series;
- TSDELTALOG(ts,i): i-periods logarithmic difference of the ts time series;
- MOVAVG(ts,i): i-periods moving average of the ts time series;
- MOVSUM(ts,i): i-periods moving sum of the ts time series;
- LOG(ts): log of the ts time series.;
- EXP(ts): exponential of the ts time series;
- ABS(ts): absolute values of the ts time series;
More details about the Model Description Language are available in MDL help pages.
Note that BIMETS classifies a model as a forward-looking model if any model equation contains the TSLEAD time series function. More details about forward-looking models are available in the "Rational Expectations Models" section of the SIMULATE help pages.LOAD_MODEL() is the BIMETS function that reads an MDL model file and creates an equivalent R data structure. Back to Klein's model example, the BIMETS LOAD_MODEL function reads the klein1.txt model as previously defined:
R> kleinModel <- LOAD_MODEL(modelText = klein1.txt)
Analyzing behaviorals...
Analyzing identities...
Optimizing...
Loaded model "klein1.txt":
3 behaviorals
3 identities
12 coefficients
...LOAD MODEL OK
As shown in the output, BIMETS counted 3 behavioral equations, 3 identities and 12 coefficients. Now in the R session there is a variable named kleinModel that contains the model structure defined in the klein1.txt variable. From now on, users can ask BIMETS about any details of this model.
For example, to gather information on the "cn" Consumption behavioral equation:
R> kleinModel$behaviorals$cn $eq [1] "cn=a1+a2*p+a3*TSLAG(p,1)+a4*(w1+w2)" $eqCoefficientsNames [1] "a1" "a2" "a3" "a4" $eqComponentsNames [1] "cn" "p" "w1" "w2" $tsrange [1] 1921 1 1941 1 $eqRegressorsNames [1] "1" "p" "TSLAG(p,1)" "(w1+w2)" $eqSimExp expression(cn[2, ] = cn__ADDFACTOR[2, ] + +cn__a1 * 1 + cn__a2 * p[2, ] + cn__a3 * (p[1, ]) + cn__a4 * (w1[2, ] + w2[2, ])) etc...
Users can always read (or carefully change) any model parameters. The LOAD_MODEL function parses behavioral and identity expressions of the MDL definition, but it also does a significant optimization. Properly reordering the model equations is a key preparatory step in the later phase of the simulation, in order to guarantee performance and convergence, if any, with the aim of minimizing the number of feedback endogenous variables (see "The Optimal Reordering" section in SIMULATE).
The LOAD_MODEL function builds the model's incidence matrix, and uses this matrix to calculate the proper evaluation order of the model equations during the simulation.
Back to the Klein's model example, the incidence matrix and the reordering of the equations are stored in the following variables:
R> kleinModel$incidence_matrix cn i w1 y p k cn 0 0 1 0 1 0 i 0 0 0 0 1 0 w1 0 0 0 1 0 0 y 1 1 0 0 0 0 p 0 0 1 1 0 0 k 0 1 0 0 0 0 R> kleinModel$vpre NULL R> kleinModel$vblocks[[1]]$vsim [1] "w1" "p" "i" "cn" "y" R> kleinModel$vblocks[[1]]$vfeed [1] "y" R> kleinModel$vblocks[[1]]$vpost [1] "k"
While simulating the Klein's model, BIMETS will iterate on the computation of, in order,w1 -> p -> i -> cn -> y (the vsim variables in the single block of equations vblocks[[1]]), by looking for convergence on y (the vfeed variable, only one in this example) that is the feedback variable for the block. If the convergence in the block is achieved, it will calculate k (the vpost variable). The vpre array in this example is empty; therefore, no equation has to be evaluated before the iterative algorithm is applied to each block of equations.
More details on the equations reordering are available in "The Optimal Reordering" section in SIMULATE and in LOAD_MODEL help pages.
Once the model has been parsed, users need to load the data of all the time series involved in the model, by using the LOAD_MODEL_DATA function. In the following example, the code defines a list of time series and loads this list into the Klein's model previously defined:
R> kleinModelData <- list(
cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,
55,50.9,45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7,
START=c(1920,1),FREQ=1),
g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,
10.2,9.3,10,10.5,10.3,11,13,14.4,15.4,22.3,
START=c(1920,1),FREQ=1),
i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,
-5.1,-3,-1.3,2.1,2,-1.9,1.3,3.3,4.9,
START=c(1920,1),FREQ=1),
k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,
210.6,215.7,216.7,213.3,207.1,202,199,197.7,199.8,
201.8,199.9,201.2,204.5,209.4,
START=c(1920,1),FREQ=1),
p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,
15.6,11.4,7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5,
START=c(1920,1),FREQ=1),
w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,
37.9,34.5,29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3,
START=c(1920,1),FREQ=1),
y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,
50.7,41.3,45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3,
START=c(1920,1),FREQ=1),
t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,
6.8,7.2,8.3,6.7,7.4,8.9,9.6,11.6,
START=c(1920,1),FREQ=1),
time=TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,
1,2,3,4,5,6,7,8,9,10,
START=c(1920,1),FREQ=1),
w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,
5.3,5.6,6,6.1,7.4,6.7,7.7,7.8,8,8.5,
START=c(1920,1),FREQ=1)
)
R> kleinModel <- LOAD_MODEL_DATA(kleinModel,kleinModelData)
Since time series and other data (e.g. regressor coefficients, error coefficients, constant adjustments, targets, instruments, etc...) are stored in the model object, users can define multiple model objects - each with its own arbitrary data - in the same R session. BIMETS makes it possible to estimate, simulate and compare results from different models with different data sets. Furthermore, users can easily save an estimated or a simulated model as a standard R variable, thus reloading it later, having all available data and time series stored in it, i.e. endogenous and exogenous time series, estimated coefficients, constant adjustments, simulation options, simulated time series, calculated instruments, targets, etc. (see also SIMULATE, STOCHSIMULATE, RENORM, OPTIMIZE)
An advanced MDL model example follows:
R> #KLEIN MODEL WITH AUTOCORRELATION, RESTRICTIONS, R> #CONDITIONAL EVALUATIONS AND LHS FUNCTIONS R> lhsKlein1.txt <- " MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions, COMMENT> conditional evaluations and LHS functions on EQ COMMENT> Exp Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> EXP(cn) = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Log Investment BEHAVIORAL> i TSRANGE 1925 1 1941 1 EQ> LOG(i) = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(TSDELTA(y)+t-w2) + c3*TSLAG(TSDELTA(y)+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Delta Gross National Product IDENTITY> y EQ> TSDELTA(y) = EXP(cn) + LOG(i) + g - t COMMENT> Profits IDENTITY> p EQ> p = TSDELTA(y) - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + LOG(i) IF> LOG(i) > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> LOG(i) <= 0 END"
See MDL help page for details.
| Estimation |
The BIMETS ESTIMATE function estimates equations that are linear in the coefficients, as specified in the behavioral equations of the model object. Coefficients can be estimated for single equations or blocks of simultaneous equations. The estimation function supports:
- Ordinary Least Squares;
- Instrumental Variables;
- Deterministic linear restrictions on the coefficients;
- Almon Polynomial Distributed Lags;
- Autocorrelation of the errors;
- Structural stability analysis (Chow tests);
Restrictions procedure derives from Lagrange Multipliers' theory, while the Cochrane-Orcutt method allows accounting for residuals autocorrelation.
The estimation of the previously defined Klein's model is shown in the following example:
R> kleinModel <- ESTIMATE(kleinModel)
Users can also estimate a selection of behavioral equations:
R> kleinModel <- ESTIMATE(kleinModel,eqList=c('cn'))
Estimate the Model klein1.txt:
the number of behavioral equations to be estimated is 1.
The total number of coefficients is 4.
_________________________________________
BEHAVIORAL EQUATION: cn
Estimation Technique: OLS
cn = 16.2366
T-stat. 12.46382 ***
+ 0.1929344 p
T-stat. 2.115273 *
+ 0.0898849 TSLAG(p,1)
T-stat. 0.9915824
+ 0.7962187 (w1+w2)
T-stat. 19.93342 ***
STATs:
R-Squared : 0.9810082
Adjusted R-Squared : 0.9776567
Durbin-Watson Statistic : 1.367474
Sum of squares of residuals : 17.87945
Standard Error of Regression : 1.02554
Log of the Likelihood Function : -28.10857
F-statistic : 292.7076
F-probability : 7.993606e-15
Akaike's IC : 66.21714
Schwarz's IC : 71.43975
Mean of Dependent Variable : 53.99524
Number of Observations : 21
Number of Degrees of Freedom : 17
Current Sample (year-period) : 1921-1 / 1941-1
Signif. codes: *** 0.001 ** 0.01 * 0.05
...ESTIMATE OK
A similar output is shown for each estimated regression. Once the estimation is completed, coefficient values, residuals, statistics, etc. are stored in the model object.
R> #print estimated coefficients
R> kleinModel$behaviorals$cn$coefficients
[,1]
a1 16.2366003
a2 0.1929344
a3 0.0898849
a4 0.7962187
R> #print residuals
R> kleinModel$behaviorals$cn$residuals
Time Series:
Start = 1921
End = 1941
Frequency = 1
[1] -0.323893544 -1.250007790 -1.565741401 -0.493503129 0.007607907
[6] 0.869096295 1.338476868 1.054978943 -0.588557053 0.282311734
[11] -0.229653489 -0.322131892 0.322281007 -0.058010257 -0.034662717
[16] 1.616497310 -0.435973632 0.210054350 0.989201310 0.785077489
[21] -2.173448309
R> #print a selection of estimate statistics
R> kleinModel$behaviorals$cn$statistics$DegreesOfFreedom
[1] 17
R> kleinModel$behaviorals$cn$statistics$StandardErrorRegression
[1] 1.02554
R> kleinModel$behaviorals$cn$statistics$CoeffCovariance
a1 a2 a3 a4
a1 1.6970227814 0.0005013886 -0.0177068887 -0.0329172192
a2 0.0005013886 0.0083192948 -0.0052704304 -0.0013188865
a3 -0.0177068887 -0.0052704304 0.0082170486 -0.0006710788
a4 -0.0329172192 -0.0013188865 -0.0006710788 0.0015955167
R> kleinModel$behaviorals$cn$statistics$AdjustedRSquared
[1] 0.9776567
R> kleinModel$behaviorals$cn$statistics$LogLikelihood
[1] -28.10857
Below is an example of a model estimation that presents coefficient restrictions, PDL, error autocorrelation, and conditional equation evaluations:
R> #define model
R> advancedKlein1.txt <-
"MODEL
COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL,
COMMENT> autocorrelation on errors, restrictions and
COMMENT> conditional equation evaluations
COMMENT> Consumption with autocorrelation on errors
BEHAVIORAL> cn
TSRANGE 1923 1 1940 1
EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2)
COEFF> a1 a2 a3 a4
ERROR> AUTO(2)
COMMENT> Investment with restrictions
BEHAVIORAL> i
TSRANGE 1923 1 1940 1
EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1)
COEFF> b1 b2 b3 b4
RESTRICT> b2 + b3 = 1
COMMENT> Demand for Labor with PDL
BEHAVIORAL> w1
TSRANGE 1923 1 1940 1
EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time
COEFF> c1 c2 c3 c4
PDL> c3 1 2
COMMENT> Gross National Product
IDENTITY> y
EQ> y = cn + i + g - t
COMMENT> Profits
IDENTITY> p
EQ> p = y - (w1+w2)
COMMENT> Capital Stock with IF switches
IDENTITY> k
EQ> k = TSLAG(k,1) + i
IF> i > 0
IDENTITY> k
EQ> k = TSLAG(k,1)
IF> i <= 0
END"
R> #load model and data
R> advancedKleinModel <- LOAD_MODEL(modelText=advancedKlein1.txt)
Analyzing behaviorals...
Analyzing identities...
Optimizing...
Loaded model "advancedKlein1.txt":
3 behaviorals
3 identities
12 coefficients
...LOAD MODEL OK
R> advancedKleinModel <- LOAD_MODEL_DATA(advancedKleinModel,kleinModelData)
Load model data "kleinModelData" into model "advancedKlein1.txt"...
...LOAD MODEL DATA OK
R> #estimate model
R> advancedKleinModel <- ESTIMATE(advancedKleinModel)
Estimate the Model advancedKlein1.txt:
the number of behavioral equations to be estimated is 3.
The total number of coefficients is 13.
_________________________________________
BEHAVIORAL EQUATION: cn
Estimation Technique: OLS
Autoregression of Order 2 (Cochrane-Orcutt procedure)
Convergence was reached in 6 / 20 iterations.
cn = 14.82685
T-stat. 7.608453 ***
+ 0.2589094 p
T-stat. 2.959808 *
+ 0.01423821 TSLAG(p,1)
T-stat. 0.1735191
+ 0.8390274 (w1+w2)
T-stat. 14.67959 ***
ERROR STRUCTURE: AUTO(2)
AUTOREGRESSIVE PARAMETERS:
Rho Std. Error T-stat.
0.2542111 0.2589487 0.9817045
-0.05250591 0.2593578 -0.2024458
STATs:
R-Squared : 0.9826778
Adjusted R-Squared : 0.9754602
Durbin-Watson Statistic : 2.256004
Sum of squares of residuals : 8.071633
Standard Error of Regression : 0.8201439
Log of the Likelihood Function : -18.32275
F-statistic : 136.1502
F-probability : 3.873514e-10
Akaike's IC : 50.6455
Schwarz's IC : 56.8781
Mean of Dependent Variable : 54.29444
Number of Observations : 18
Number of Degrees of Freedom : 12
Current Sample (year-period) : 1923-1 / 1940-1
Signif. codes: *** 0.001 ** 0.01 * 0.05
_________________________________________
BEHAVIORAL EQUATION: i
Estimation Technique: OLS
i = 0.5348561
T-stat. 0.06197295
+ 0.6267204 p
T-stat. 4.835884 ***
+ 0.3732796 TSLAG(p,1)
T-stat. 2.88029 *
- 0.0796483 TSLAG(k,1)
T-stat. -1.871304
RESTRICTIONS:
b2+b3=1
RESTRICTIONS F-TEST:
F-value : 5.542962
F-prob(1,14) : 0.03368297
STATs:
R-Squared : 0.9009016
Adjusted R-Squared : 0.8876885
Durbin-Watson Statistic : 1.284709
Sum of squares of residuals : 23.40087
Standard Error of Regression : 1.249023
Log of the Likelihood Function : -27.90251
F-statistic : 68.18238
F-probability : 2.954599e-08
Akaike's IC : 63.80501
Schwarz's IC : 67.3665
Mean of Dependent Variable : 1.111111
Number of Observations : 18
Number of Degrees of Freedom : 15
Current Sample (year-period) : 1923-1 / 1940-1
Signif. codes: *** 0.001 ** 0.01 * 0.05
_________________________________________
BEHAVIORAL EQUATION: w1
Estimation Technique: OLS
w1 = 2.916775
T-stat. 1.808594
+ 0.4229623 (y+t-w2)
T-stat. 10.32315 ***
+ c3 TSLAG(y+t-w2,1)
PDL
+ 0.1020647 time
T-stat. 3.048413 **
PDL:
c3 1 2
Distributed Lag Coefficient: c3
Lag Coeff. Std. Error T-stat.
0 0.1292072 0.06348684 2.035181
1 0.01035948 0.04266269 0.2428229
SUM 0.1395667 0.03801893
STATs:
R-Squared : 0.9806112
Adjusted R-Squared : 0.9746454
Durbin-Watson Statistic : 2.038182
Sum of squares of residuals : 6.59422
Standard Error of Regression : 0.7122132
Log of the Likelihood Function : -16.50329
F-statistic : 164.3727
F-probability : 5.454803e-11
Akaike's IC : 45.00658
Schwarz's IC : 50.34881
Mean of Dependent Variable : 36.41667
Number of Observations : 18
Number of Degrees of Freedom : 13
Current Sample (year-period) : 1923-1 / 1940-1
Signif. codes: *** 0.001 ** 0.01 * 0.05
...ESTIMATE OK
| Structural Stability |
One of the main purposes of econometric modeling is its use for forecast and policy evaluation and, to this end, the stability of any behavioral equation parameters over time should be verified. In order to check for structural stability two different procedures, which can be derived from the so-called Chow-tests, are applied.
Given a sample of observations (i.e. the base TSRANGE) and selecting an arbitrary forward extension (i.e. the extended TSRANGE) we can perform the same regression by using these two time ranges.
In general, a stability analysis is carried on in the following ways:
- comparing the parameter estimates arising from the two regressions: this is known as the covariance analysis;
- checking the accuracy of the forecast for the dependent variable in the extended TSRANGE, using the estimates produced in the base TSRANGE: this is known as the predictive power test.
The test statistic follows the F distribution and can be performed during the ESTIMATE() function execution by using the CHOWTEST argument set to TRUE (more details in the ESTIMATE help page).
Example:
#chow test for the consumption equation
#base TSRANGE set to 1921/1935
R> kleinModelChow <- ESTIMATE(kleinModel
,eqList='cn'
,TSRANGE=c(1921,1,1935,1)
,forceTSRANGE=TRUE
,CHOWTEST=TRUE)
Estimate the Model klein1.txt:
the number of behavioral equations to be estimated is 1.
The total number of coefficients is 4.
_________________________________________
BEHAVIORAL EQUATION: cn
Estimation Technique: OLS
cn = 13.1275
T-stat. 6.5046 ***
+ 0.16698 p
T-stat. 2.18304
+ 0.0885684 TSLAG(p,1)
T-stat. 0.975042
+ 0.887964 (w1+w2)
T-stat. 12.61 ***
STATs:
R-Squared : 0.978728
Adjusted R-Squared : 0.972926
Durbin-Watson Statistic : 1.38
Sum of squares of residuals : 6.9186
Standard Error of Regression : 0.793072
Log of the Likelihood Function : -15.4803
F-statistic : 168.7
F-probability : 1.77673e-09
Akaike's IC : 40.9606
Schwarz's IC : 44.5009
Mean of Dependent Variable : 50.9133
Number of Observations : 15
Number of Degrees of Freedom : 11
Current Sample (year-period) : 1921-1 / 1935-1
Signif. codes: *** 0.001 ** 0.01 * 0.05
STABILITY ANALYSIS:
Behavioral equation: cn
Chow test:
Sample (auto) : 1936-1 / 1941-1
F-value : 4.48873
F-prob(6,17) : 0.00668723
Predictive Power:
Date, Prd., Actual , Predict , Error , Std. Error, T-stat
1936, 1 , 57.7 , 56.5544 , 1.14564 , 1.01181 , 1.13227
1937, 1 , 58.7 , 59.931 , -1.23099 , 1.0201 , -1.20673
1938, 1 , 57.5 , 57.9721 , -0.472122 , 0.968638 , -0.487409
1939, 1 , 61.6 , 61.5207 , 0.0793139 , 1.20048 , 0.0660685
1940, 1 , 65 , 65.3957 , -0.395718 , 1.24227 , -0.318545
1941, 1 , 69.7 , 73.7965 , -4.09655 , 1.6693 , -2.45405
...ESTIMATE OK
| Simulation |
The simulation of an econometric model basically consists in solving the system of the equations describing the model for each time period in the specified time interval. Since the equations may not be linear in the variables, and since the graph derived from the incidence matrix may be cyclic, the usual methods based on linear algebra are not applicable. The simulation must be solved by using an iterative algorithm.
BIMETS simulation capabilities support:
- Static simulations: a static multiple equation simulation, in which the historical values for the lagged endogenous variables are used in the solutions of subsequent periods;
- Dynamic simulations: a dynamic simulation, in which the simulated values for the lagged endogenous variables are used in the solutions of subsequent periods;
- Forecast simulations: similar to dynamic simulation, but during the initialization of the iterative algorithm the starting values of endogenous variables in a period are set equal to the simulated values of the previous period. This allows the simulation of future endogenous observations, i.e. the forecast;
- Residuals check: a single period, single equation simulation; simulated time series in output are just the computation of the RHS (right-hand-side) of their equation, by using the historical values of the involved time series and by accounting for error autocorrelation and PDLs, if any;
- Stochastic Simulation: see STOCHSIMULATE;
- Partial or total exogenization of endogenous variables: in the provided time interval (i.e. partial exog.) or in whole simulation time range (i.e. total exog.), the values of the selected endogenous variables can be definitely set to their historical values, by excluding their equations from the iterative algorithm of simulation;
- Constant adjustment of endogenous variables (add-factors): adds up a new exogenous time series (i.e. the "constant adjustment") in the equation of the selected endogenous variables.
- Gauss-Seidel and Newton-Raphson simulation algorithms: the Gauss-Seidel algorithm is simple, robust, and works well for many backward-looking macro-econometric models. Equations are evaluated as-is in a proper order until the convergence, if any, is verified on feedback variables. It is slower than Newton algorithms for a very low convergence criterion, and fails to find a convergence for a small set of econometric models, even when a convergence exists. The Newton-Raphson algorithm allows users to solve a broader set of macro-econometric models than the Gauss-Seidel algorithm. Moreover, it is usually faster than the Gauss-Seidel algorithm (on modern computers, users must simulate an extensive econometric model with a low convergence criterion to appreciate the speedup). This type of algorithm requires the construction and the inversion of the Jacobian matrix for the feedback variables; thus, in some scenarios, numerical issues can arise, and users are required to manually exclude some feedback variables from the Jacobian matrix by using the JacobianDrop argument of the SIMULATE procedure.
More details are available in the SIMULATE help page.
Back to Kelin's model example, let's forecast the GNP (i.e. the "y" endogenous variable, originally referred as "Net national income, measured in billions of 1934 dollars", pag. 141 in "Economic Fluctuations in the United States" by L. R. Klein, Wiley and Sons Inc., New York, 1950) up to 1943:
R> #FORECAST GNP in 1942:1944
R> #we need to extend exogenous variables in 1942 up to 1944
R> kleinModel$modelData <- within(kleinModel$modelData,{
w2 = TSEXTEND(w2, UPTO=c(1944,1),EXTMODE='CONSTANT')
t = TSEXTEND(t, UPTO=c(1944,1),EXTMODE='CONSTANT')
g = TSEXTEND(g, UPTO=c(1944,1),EXTMODE='CONSTANT')
time = TSEXTEND(time,UPTO=c(1944,1),EXTMODE='LINEAR')
})
R> #simulate model
R> kleinModel <- SIMULATE(kleinModel
,simType='FORECAST'
,TSRANGE=c(1941,1,1944,1)
,simConvergence=0.00001
,simIterLimit=100
)
Simulation: 100.00 %
...SIMULATE OK
R> #get forecasted GNP
R> TABIT(kleinModel$simulation$y)
Date, Prd., kleinModel$simulation$y
1941, 1 , 95.41613
1942, 1 , 106.8923
1943, 1 , 107.4302
1944, 1 , 100.7512
Below is an example of advanced simulation using the NEWTON algorithm:
R> #DYNAMIC NEWTON SIMULATION EXAMPLE
R> #WITH EXOGENIZATION AND CONSTANT ADJUSTMENTS
R> #define exogenization list
R> #'cn' exogenized in 1923-1925
R> #'i' exogenized in whole TSRANGE
R> exogenizeList <- list(
cn = c(1923,1,1925,1),
i = TRUE
)
R> #define add-factor list
R> #cn add-factor will be 1 in 1923 and -1 in 1924
R> #y add-factor will be 0.1 in 1926, -0.1 in 1927 and -0.5 in 1928
R> constantAdjList <- list(
cn = TIMESERIES(1,-1,START=c(1923,1),FREQ='A'),
y = TIMESERIES(0.1,-0.1,-0.5,START=c(1926,1),FREQ='A')
)
R> #simulate model
R> kleinModel <- SIMULATE(kleinModel
,simAlgo='NEWTON'
,simType='DYNAMIC'
,TSRANGE=c(1923,1,1941,1)
,simConvergence=0.00001
,simIterLimit=100
,Exogenize=exogenizeList
,ConstantAdjustment=constantAdjList
)
| Rational Expectations |
BIMETS classifies a model as a forward-looking model if any model equation contains the TSLEAD time series function. Forward-looking models assume that economic agents have complete knowledge of an economic system and calculate the future value of economic variables correctly according to that knowledge. Thus, forward-looking models are called also rational expectations models and, in macro-econometric models, model-consistent
expectations.
In forward-looking models, simulation complexity arises, and all simulation periods must be solved simultaneously because equations can contain references to past and future values. Thus, given N simulation periods requested by the user, each model equation must be replicated N-1 times and modified before the simulation takes place, accounting for lead transformations. Finally, the extended model must be simulated as a single block of equations.
Internal data structures, such as the incidence and the Jacobian matrix, and the reordering arrays vpre and vblocks (described in the "The Optimal Reordering" section in SIMULATE help page), grow with the number of simulation periods requested. Therefore, they can only be calculated when a new simulation is requested rather than when the model MDL definition is parsed, further extending computational time.
For technical details, see "Rational Expectations" section in SIMULATE. An example for a Klein-like forward-looking model simulation follows:
########################################################
#EXAMPLE OF FORWARD-LOOKING KLEIN-LIKE MODEL
#HAVING RATIONAL EXPECTATION ON INVESTMENTS
#define model
kleinLeadModelDefinition<-
"MODEL
COMMENT> Klein Model 1 of the U.S. Economy
COMMENT> Consumption
BEHAVIORAL> cn
TSRANGE 1921 1 1941 1
EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2)
COEFF> a1 a2 a3 a4
COMMENT> Investment with TSLEAD
IDENTITY> i
EQ> i = (MOVAVG(i,2)+TSLEAD(i))/2
COMMENT> Demand for Labor
BEHAVIORAL> w1
TSRANGE 1921 1 1941 1
EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time
COEFF> c1 c2 c3 c4
COMMENT> Gross National Product
IDENTITY> y
EQ> y = cn + i + g - t
COMMENT> Profits
IDENTITY> p
EQ> p = y - (w1+w2)
COMMENT> Capital Stock
IDENTITY> k
EQ> k = TSLAG(k,1) + i
END"
#load model and model data
kleinLeadModel<-LOAD_MODEL(modelText=kleinLeadModelDefinition)
kleinLeadModel<-LOAD_MODEL_DATA(kleinLeadModel,kleinModelData)
#estimate model
kleinLeadModel<-ESTIMATE(kleinLeadModel, quietly = TRUE)
#set expected value of 2 for Investment in 1931
#(note that simulation TSRANGE spans up to 1930)
kleinLeadModel$modelData$i[[1931,1]]<-2
#simulate model
kleinLeadModel<-SIMULATE(kleinLeadModel
,TSRANGE=c(1924,1,1930,1))
#print simulated investments
TABIT(kleinLeadModel$simulation$i)
| Stochastic Simulation |
Forecasts produced by structural econometric models are subject to several sources of error, such as random disturbance term of each stochastic equation, errors in estimated coefficients, errors in forecasts of exogenous variables, errors in preliminary data and mis-specification of the model.
The forecast error depending on the structural disturbances can be analyzed by using the stochastic simulation procedure.
The deterministic simulation is the simultaneous solution of an econometric model obtained by applying, for each stochastic (behavioral) equation, the expected values of the structural disturbances, which are all zero by assumption. In the BIMETS STOCHSIMULATE stochastic simulation, the structural disturbances are given values that have specified stochastic properties. The error terms of the estimated behavioral equation of the model are appropriately perturbed. Identity equations and exogenous variables can be as well perturbed by disturbances that have specified stochastic properties. The model is then solved for each data set with different values of the disturbances. Finally, mean and standard deviation are computed for each simulated endogenous variable.
In terms of computational efficiency, the procedure takes advantage of the fact that multiple datasets are bound together in matrices. Therefore, to achieve a global convergence, the iterative simulation algorithm is executed once for all perturbed datasets. This solution can be viewed as a sort of a SIMD (i.e. Single Instruction Multiple Data) parallel simulation: STOCHSIMULATE function transforms time series into matrices; consequently, the procedure can easily bind multiple datasets by column. At the same time, a single run ensures a fast code execution. Finally, each column in the output matrices represents a stochastic realization.
By using the StochStructure argument of this function, users can define a stochastic structure for the disturbances. For each variable of the model, users can provide a distinct probability distribution for the disturbance, and a specific time range of application. Mean and standard deviation for each simulated endogenous time series will be stored in the stochastic_simulation element of the output model object; all the stochastic realizations will be stored in the simulation_MM element of the output model object as named matrices.
In the following figure, the advanced Klein model (see code example), has been perturbed during the forecast operation by applying a normal disturbance to the endogenous Consumption behavioral cn add-factor in year 1942, and a uniform disturbance to the exogenous Government Expenditure time series g along all the simulation TSRANGE. The normal disturbance applied to the cn behavioral has a zero mean and a standard deviation equal to the behavioral regression standard error,
i.e. advancedKleinModel$behaviorals$cn$statistics$StandardErrorRegression, thus roughly replicating the ESTIMATE regression error during the current perturbation (not accounting for inter-equations cross-covariance).
R> #we want to perform a stochastic forecast of the GNP up to 1944
R> #we will add normal disturbances to endogenous Consumption 'cn'
R> #in 1942 by using its regression standard error
R> #we will add uniform disturbances to exogenous Government Expenditure 'g'
R> #in whole TSRANGE
R> nSD=advancedKleinModel$behaviorals$cn$statistics$StandardErrorRegression
R> myStochStructure <- list(
cn=list(
TSRANGE=c(1942,1,1942,1),
TYPE='NORM',
PARS=c(0,nSD)
),
g=list(
TSRANGE=TRUE,
TYPE='UNIF',
PARS=c(-1,1)
)
)
R> #we need to extend exogenous variables up to 1944
R> advancedKleinModel$modelData <- within(advancedKleinModel$modelData,{
w2 = TSEXTEND(w2, UPTO=c(1944,1),EXTMODE='CONSTANT')
t = TSEXTEND(t, UPTO=c(1944,1),EXTMODE='LINEAR')
g = TSEXTEND(g, UPTO=c(1944,1),EXTMODE='CONSTANT')
k = TSEXTEND(k, UPTO=c(1944,1),EXTMODE='LINEAR')
time = TSEXTEND(time,UPTO=c(1944,1),EXTMODE='LINEAR')
})
R> #stochastic model forecast
R> advancedKleinModel <- STOCHSIMULATE(advancedKleinModel
,simType='FORECAST'
,TSRANGE=c(1941,1,1944,1)
,StochStructure=myStochStructure
,StochSeed=123
)
R> #print mean and standard deviation of forecasted GNP
R> with(advancedKleinModel$stochastic_simulation,TABIT(y$mean, y$sd))
Date, Prd., y$mean , y$sd
1941, 1 , 125.5045 , 4.250935
1942, 1 , 173.2946 , 9.2632
1943, 1 , 185.9602 , 11.87774
1944, 1 , 141.0807 , 11.6973
R> #print the unperturbed forecasted GNP along with the
R> #first 5 perturbed realizations
R> with(advancedKleinModel$simulation_MM,print(y[,1:6]))
| Multipliers Analysis |
The BIMETS MULTMATRIX function computes the matrix of both impact and interim multipliers, for a selected set of endogenous variables (i.e. TARGET) with respect to a selected set of exogenous variables (i.e. INSTRUMENT), by subtracting the results from different simulations in each period of the provided time range (i.e. TSRANGE). The simulation algorithms are the same as those used for the SIMULATE operation.
The MULTMATRIX procedure is articulated as follows:
1. simultaneous simulations are done;
2. the first simulation establishes the base line solution (without shocks);
3. the other simulations are done with shocks applied to each of the INSTRUMENT one at a time for every period in TSRANGE;
4. each simulation follows the defaults described in the SIMULATE help page, but has to be STATIC for the IMPACT multipliers and DYNAMIC for INTERIM multipliers;
5. given MM_SHOCK shock amount as a very small positive number, derivatives are computed by subtracting the base line solution of the TARGET from the shocked solution, then dividing by the value of the base line INSTRUMENT times the MM_SHOCK;
BIMETS users can also declare an endogenous variable as the INSTRUMENT variable. In this case, the constant adjustment (see SIMULATE) related to the provided endogenous variable will be used as the INSTRUMENT exogenous variable.
Back to our Klein's model example, we can calculate impact multipliers of Government Expenditure "g" and Government Wage Bill "w2" with respect of Consumption "cn" and Gross National Product "y" in the year 1941 by using the previously estimated model:
R> kleinModel <- MULTMATRIX(kleinModel,
symType='STATIC',
TSRANGE=c(1941,1,1941,1),
INSTRUMENT=c('w2','g'),
TARGET=c('cn','y')
)
Multiplier Matrix: 100.00 %
...MULTMATRIX OK
R> kleinModel$MultiplierMatrix
w2_1 g_1
cn_1 0.4540346 1.671956
y_1 0.2532000 3.653260
Results show that the impact multiplier of "y" with respect to "g" is +3.65. If we change the Government Expenditure "g" value in 1941 from 22.3 (his historical value) to 23.3 (+1), then the simulated Gross National Product "y" in 1941 changes from 95.2 to 99, thusly roughly confirming the +3.65 impact multiplier. Note that "g" only appears once in the model definition, and only in the "y" equation, with a coefficient equal to one (Keynes would approve).
An interim-multiplier example follows:
R> #multi-period interim multipliers
R> kleinModel <- MULTMATRIX(kleinModel,
TSRANGE=c(1940,1,1941,1),
INSTRUMENT=c('w2','g'),
TARGET=c('cn','y'))
Multiplier Matrix: 100.00 %
...MULTMATRIX OK
R> #output multipliers matrix (note the zeros where the period
R> #of the INSTRUMENT is greater than the period of the TARGET)
R> kleinModel$MultiplierMatrix
w2_1 g_1 w2_2 g_2
cn_1 0.4478202 1.582292 0.0000000 0.000000
y_1 0.2433382 3.510971 0.0000000 0.000000
cn_2 -0.3911001 1.785042 0.4540346 1.671956
y_2 -0.6251177 2.843960 0.2532000 3.653260
| Endogenous Targeting |
The endogenous targeting of econometric models consists of solving the model while interchanging the role of one or more endogenous variables with an equal number of exogenous variables.
The BIMETS RENORM procedure determines the values for the INSTRUMENT exogenous variables that allow the objective TARGET endogenous values to be achieved, with respect to the constraints given by the model equations (see MDL).
This is an approach to economic and monetary policy analysis, and is based on two assumptions:
1. there exists a desired level for a set of the n endogenous variables defined as TARGET;
2. there exists a set of the n exogenous variables defined as INSTRUMENT;
Given these premises, the endogenous targeting process consists in determining the values of the exogenous variables chosen as INSTRUMENT allowing us to achieve the desired values for the endogenous variables designated as TARGET. In other words the procedure allows users to exchange the role of exogenous and endogenous among a set of variables pairs.
Given a list of exogenous INSTRUMENT variables and a list of TARGET endogenous time series, the iterative procedure can be split into the following steps:
1. Computation of the multipliers matrix MULTMAT of the TARGET endogenous variables with respect to the INSTRUMENT exogenous variables (this is a square matrix by construction);
2. Solution of the linear system (if any):
MULTMAT TARGET , where are the exogenous variables in the INSTRUMENT list and are the endogenous variables that have a related target in the TARGET list, given i the current iteration;
3. Simulation of the model with the new set of exogenous variables computed in step 2, then a convergence check by comparing the subset of endogenous variables arising from this simulation and the related time series in TARGET list. If the convergence condition is satisfied, or the maximum number of iterations is reached, the algorithm will stop, otherwise it will go back to step 1;
Users can also declare an endogenous variable as an INSTRUMENT variable. In this case, the constant adjustment (see SIMULATE) related to the provided endogenous variable will be used as the instrument exogenous variable. This procedure is particularly suited for the automatic computation of the add-factors needed to fine tune the model into a baseline path and to improve the forecasting accuracy.
If the convergence condition is satisfied, the RENORM procedure will return the INSTRUMENT time series allowing us to achieve the desired values for endogenous variables designated as TARGET.
Back to our Klein's model example, we can perform the endogenous targeting of the previously estimated model. First of all, the targets must be defined:
R> #we want an arbitrary value on Consumption of 66 in 1940 and 78 in 1941
R> #we want an arbitrary value on GNP of 77 in 1940 and 98 in 1941
R> kleinTargets <- list(
cn = TIMESERIES(66,78,START=c(1940,1),FREQ=1),
y = TIMESERIES(77,98,START=c(1940,1),FREQ=1)
)
Then, we can perform the model endogenous targeting by using the "w2" (Wage Bill of the Government Sector) and the "g" (Government Expenditure) exogenous variables as INSTRUMENT, in the years 1940 and 1941:
R> kleinModel <- RENORM(kleinModel
,INSTRUMENT = c('w2','g')
,TARGET = kleinTargets
,TSRANGE = c(1940,1,1941,1)
,simIterLimit = 100
)
Once RENORM completes, the calculated values of exogenous INSTRUMENT allowing us to achieve the desired endogenous TARGET values are stored in the model:
R> with(kleinModel,TABIT(modelData$w2,
renorm$INSTRUMENT$w2,
modelData$g,
renorm$INSTRUMENT$g,
TSRANGE=c(1940,1,1941,1)
)
)
Date, Prd., modelData$w2, renorm$INSTRUMENT$w2, modelData$g, renorm$INSTRUMENT$g
1940, 1 , 8 , 7.413331 , 15.4 , 16.1069
1941, 1 , 8.5 , 9.3436 , 22.3 , 22.65985
So, if we want to achieve on "cn" (Consumption) an arbitrary simulated value of 66 in 1940 and 78 in 1941, and if we want to achieve on "y" (GNP) an arbitrary simulated value of 77 in 1940 and 98 in 1941, we need to change exogenous "w2" (Wage Bill of the Government Sector) from 8 to 7.41 in 1940 and from 8.5 to 9.34 in 1941, and we need to change exogenous "g" (Government Expenditure) from 15.4 to 16.1 in 1940 and from 22.3 to 22.66 in 1941.
Let's verify:
R> #create a new model
R> kleinRenorm <- kleinModel
R> #get instruments to be used
R> newInstruments <- kleinModel$renorm$INSTRUMENT
R> #change exogenous by using new instruments data
R> kleinRenorm$modelData <- within(kleinRenorm$modelData,
{
w2[[1940,1]]=newInstruments$w2[[1940,1]]
w2[[1941,1]]=newInstruments$w2[[1941,1]]
g[[1940,1]] =newInstruments$g[[1940,1]]
g[[1941,1]] =newInstruments$g[[1941,1]]
}
)
R> #users can also replace last two commands with:
R> #kleinRenorm$modelData <- kleinRenorm$renorm$modelData
R> #simulate the new model
R> kleinRenorm <- SIMULATE(kleinRenorm
,TSRANGE=c(1940,1,1941,1)
,simConvergence=0.00001
,simIterLimit=100
)
Simulation: 100.00 %
...SIMULATE OK
R> #verify targets are achieved
R> with(kleinRenorm$simulation,
TABIT(cn,y)
)
Date, Prd., cn , y
1940, 1 , 66.01116 , 77.01772
1941, 1 , 78.02538 , 98.04121
| Optimal Control |
An approach to policy evaluation is via a so-called "social welfare function". This approach relaxes the assumptions of the instruments-targets framework, i.e. the RENORM procedure. Rather than assuming specific desired targets for some endogenous variables, it assumes the existence of a social welfare function determining a scalar measure of performance based on both endogenous and policy (exogenous) variables.
The social welfare function can incorporate information about tradeoffs in objectives that are not allowed by the RENORM instruments-targets approach.
BIMETS supplies the OPTIMIZE procedure in order to perform optimal control exercises on econometric models.
The optimization consists of maximizing a social welfare function, i.e. the objective-function, depending on exogenous and (simulated) endogenous variables, subject to user constraints plus the constraints imposed by the econometric model equations. Users are allowed to define constraints and objective-functions of any degree, and are allowed to provide different constraints and objective-functions in different optimization time periods.
The core of the OPTIMIZE procedure is based on a Monte Carlo method that takes advantage of the STOCHSIMULATE procedure. Policy variables, i.e. INSTRUMENT, are uniformly perturbed in the range defined by the user-provided boundaries, then the INSTRUMENT values that i) verify the user-provided constraints and ii) maximize the objective-functions are selected and stored into the optimize element of the output BIMETS model.
In the following figure, the scatter plot is populated with 2916 objective function stochastic realizations, computed by using the example code at the end of this section; the 210.58 local maximum is highlighted
(i.e. advancedKleinModel$optimize$optFunMax in code example).
In this example:
i) The objective function definition is:
given as the simulated Gross National Product, as the simulated Consumption and as the exogenous Government Expenditure: the basic idea is to maximize Consumption, and secondarily the Gross National Product, while reducing the Government Expenditure;
ii) The INSTRUMENT variables are the Consumption "booster" (i.e. the add-factor, not to be confused with the simulated Consumption in the objective function) and the Government Expenditure, defined over the following domains: , ;
iii) The following restrictions are applied to the INSTRUMENT: , given as the Consumption "booster" (i.e. the add-factor) and as the Government Expenditure;
The figure clearly shows that non-linear restrictions have been applied, and that non-computable objective functions have been discarded, e.g. the stochastic realizations having due to the square root operation in the objective function, given instrument .
An example of an optimal control exercise applied to the previoously defined advancedKleinModel follows:
R> #reset time series of the model object that have been
R> #modified in the stochastic simulation section
R> advancedKleinModel <- LOAD_MODEL_DATA(advancedKleinModel,kleinModelData)
R> #we want to maximize the non-linear objective function:
R> #f()=(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5
R> #in 1942 by using INSTRUMENT cn in range (-5,5)
R> #(cn is endogenous so we use the add-factor)
R> #and g in range (15,25)
R> #we will also impose the following non-linear restriction:
R> #g+(cn^2)/2<27 & g+cn>17
R> #we need to extend exogenous variables up to 1942
R> advancedKleinModel$modelData <- within(advancedKleinModel$modelData,{
w2 = TSEXTEND(w2, UPTO=c(1942,1),EXTMODE='CONSTANT')
t = TSEXTEND(t, UPTO=c(1942,1),EXTMODE='LINEAR')
g = TSEXTEND(g, UPTO=c(1942,1),EXTMODE='CONSTANT')
k = TSEXTEND(k, UPTO=c(1942,1),EXTMODE='LINEAR')
time = TSEXTEND(time,UPTO=c(1942,1),EXTMODE='LINEAR')
})
R> #define INSTRUMENT and boundaries
R> myOptimizeBounds <- list(
cn=list(TSRANGE=TRUE,
BOUNDS=c(-5,5)),
g=list(TSRANGE=TRUE,
BOUNDS=c(15,25))
)
R> #define restrictions
R> myOptimizeRestrictions <- list(
myRes1=list(
TSRANGE=TRUE,
INEQUALITY='g+(cn^2)/2<27 & g+cn>17')
)
R> #define objective function
R> myOptimizeFunctions <- list(
myFun1=list(
TSRANGE=TRUE,
FUNCTION='(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5')
)
R> #Monte-Carlo optimization by using 10000 stochastic realizations
R> #and 1E-4 convergence criterion
R> advancedKleinModel <- OPTIMIZE(advancedKleinModel
,simType = 'FORECAST'
,TSRANGE=c(1942,1,1942,1)
,simConvergence= 1E-4
,simIterLimit = 1000
,StochReplica = 10000
,StochSeed = 123
,OptimizeBounds = myOptimizeBounds
,OptimizeRestrictions = myOptimizeRestrictions
,OptimizeFunctions = myOptimizeFunctions)
OPTIMIZE(): optimization boundaries for the add-factor of endogenous
variable "cn" are (-5,5) from year-period 1942-1 to 1942-1.
OPTIMIZE(): optimization boundaries for the exogenous
variable "g" are (15,25) from year-period 1942-1 to 1942-1.
OPTIMIZE(): optimization restriction "myRes1" is active
from year-period 1942-1 to 1942-1.
OPTIMIZE(): optimization objective function "myFun1" is active
from year-period 1942-1 to 1942-1.
Optimize: 100.00 %
OPTIMIZE(): 2916 out of 10000 objective function realizations (29%)
are finite and verify the provided restrictions.
...OPTIMIZE OK
R> #print local maximum
R> advancedKleinModel$optimize$optFunMax
[1] 210.5755
R> #print INSTRUMENT that allow local maximum to be achieved
R> advancedKleinModel$optimize$INSTRUMENT
$cn
Time Series:
Start = 1942
End = 1942
Frequency = 1
[1] 2.032203
$g
Time Series:
Start = 1942
End = 1942
Frequency = 1
[1] 24.89773
R> #LET'S VERIFY RESULTS
R> #copy into modelData the computed INSTRUMENT
R> #that allow to maximize the objective function
R> advancedKleinModel$modelData <- advancedKleinModel$optimize$modelData
R> #simulate the model by using the new INSTRUMENT
R> #note: we used cn add-factor as OPTIMIZE instrument, so we need
R> #to pass the computed cn add-factor to the SIMULATE call
R> newConstantAdjustment <- advancedKleinModel$optimize$ConstantAdjustment
R> advancedKleinModel <- SIMULATE(advancedKleinModel
,simType = 'FORECAST'
,TSRANGE = c(1942,1,1942,1)
,simConvergence = 1E-5
,simIterLimit = 1000
,ConstantAdjustment = newConstantAdjustment)
R> #calculate objective function by using the SIMULATE output time series
R> #(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5
R> y <- advancedKleinModel$simulation$y
R> cn <- advancedKleinModel$simulation$cn
R> g <- advancedKleinModel$modelData$g
R> optFunTest <- (y-110)+(cn-90)*abs(cn-90)-(g-20)^0.5
R> #verify computed max is equal to optimization max
R> #(in the following command TSPROJECT could be omitted because
R> #myFun1$TSRANGE = TRUE)
R> abs(sum(TSPROJECT(optFunTest
,TSRANGE=c(1942,1,1942,1)
,ARRAY = TRUE)
) - advancedKleinModel$optimize$optFunMax) < 1E-4
[1] TRUE
| Package: | bimets - Time Series And Econometric Modeling In R |
| Type: | Package |
| License: | GPL-3 |
BIMETS estimation and simulation results have been compared to the output results of leading commercial econometric software by using several large and complex models.
The models used in the comparison have more than:
+100 behavioral equations;
+700 technical identities;
+500 coefficients;
+1000 time series of endogenous and exogenous variables;
In these models, there are equations with restricted coefficients, polynomial distributed lags, error autocorrelation, and conditional evaluation of technical identities; all models have been simulated in static, dynamic, and forecast mode, with exogenization and constant adjustments of endogenous variables through the use of BIMETS capabilities.
In the +800 endogenous simulated time series over the +20 simulated periods (i.e. more than 16.000 simulated observations), the average percentage difference between BIMETS and leading commercial software results has a magnitude of . The difference between results calculated by using different commercial software has the same average magnitude.
Several advanced econometric exercises on the US Federal Reserve FRB/US econometric model (e.g., dynamic simulation in a monetary policy shock, rational expectations, endogenous targeting, stochastic simulation, etc.) are available in the "US Federal Reserve quarterly model (FRB/US) in R with bimets" vignette.
BIMETS stands for Bank of Italy Model Easy Time Series; it does not depend on compilers or third-party software so it can be freely downloaded and installed on Linux, MS Windows(R) and Mac OSX(R), without any further requirements.
More details in:
- MDL
- LOAD_MODEL
- ESTIMATE
- SIMULATE
- STOCHSIMULATE
- MULTMATRIX
- RENORM
- OPTIMIZE
Disclaimer: The views and opinions expressed in these pages are those of the authors and do not necessarily reflect the official policy or position of the Bank of Italy. Examples of analysis performed within these pages are only examples. They should not be utilized in real-world analytic products as they are based only on very limited and dated open source information. Assumptions made within the analysis are not reflective of the position of the Bank of Italy.
Andrea Luciani <[email protected]>
Roberto Stok <[email protected]>
This function returns the array built with input argument values. Input can be time series, numerical arrays, or strings.
A1D(..., length = NULL, avoidCompliance = FALSE)A1D(..., length = NULL, avoidCompliance = FALSE)
... |
Input argument list.
This function accepts strings, time series, objects of class |
length |
Length of output array, that must be greater than the sum of each input argument size: if the length of the output array is provided, than the output array will be eventually filled with zeros. |
avoidCompliance |
If |
This function returns an array of the same class of the input.
NOELSis.bimetsBIMETS indexingTIMESERIESTSDATESLOCSNAMELISTINTSTSINFOTSLOOKTABITELIMELSINDEXNUM
n<-10; #create ts ts1<-TSERIES(rnorm(n),START=c(2000,1),FREQ=1) #create A1D() array with scalars, ts, and NA out_a1d<-A1D(length=25, ts1, 1, -8.9, NA) print(out_a1d) #same example no length specified out_a1d<-A1D(ts1, 1, -8.9, NA) print(out_a1d) #strings example out_a1d<-A1D(length=5,'aa','bb','ccc') print(out_a1d)n<-10; #create ts ts1<-TSERIES(rnorm(n),START=c(2000,1),FREQ=1) #create A1D() array with scalars, ts, and NA out_a1d<-A1D(length=25, ts1, 1, -8.9, NA) print(out_a1d) #same example no length specified out_a1d<-A1D(ts1, 1, -8.9, NA) print(out_a1d) #strings example out_a1d<-A1D(length=5,'aa','bb','ccc') print(out_a1d)
This function returns a yearly aggregated time series, by using as input a semiannual, quarterly, monthly or daily time series.
ANNUAL(x = NULL, fun = NULL, avoidCompliance = FALSE, ...) YEARLY(x = NULL, fun = NULL, avoidCompliance = FALSE, ...)ANNUAL(x = NULL, fun = NULL, avoidCompliance = FALSE, ...) YEARLY(x = NULL, fun = NULL, avoidCompliance = FALSE, ...)
x |
Input time series, that must satisfy the compliance control check defined in |
fun |
STOCK: the output value of a year is equal to the value of the input time series in the last period of the same year |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a yearly BIMETS time series.
SEMIANNUALQUARTERLYMONTHLYDAILY
#TS DAILY TO ANNUAL n<-366 ts1<-TIMESERIES(0:n,START=c(2000,1),FREQ='D') ts1[10]<-NA TABIT(ANNUAL(ts1,fun='NAVE')) #TS DAILY TO ANNUAL n<-36 ts1<-TIMESERIES(0:n,START=c(2000,1),FREQ='M') ts1[10]<-NA TABIT(YEARLY(ts1,fun='SUM'))#TS DAILY TO ANNUAL n<-366 ts1<-TIMESERIES(0:n,START=c(2000,1),FREQ='D') ts1[10]<-NA TABIT(ANNUAL(ts1,fun='NAVE')) #TS DAILY TO ANNUAL n<-36 ts1<-TIMESERIES(0:n,START=c(2000,1),FREQ='M') ts1[10]<-NA TABIT(YEARLY(ts1,fun='SUM'))
This function tries to convert a time series of class ts() or xts() into a BIMETS time series that satisfy the compliance control check defined in is.bimets
All the information in the input time series will be preserved.
Input time series must be of class ts() or xts(), and will be converted in the BIMETS class-type specified in the global option BIMETS_CONF_CCT (see BIMETS configuration).
If the input time series has a temporal discontinuity (i.e. a missing pair Date-Value in the case of xts() time series) then the missing pair Date-Value is inserted in the output time series with a missing value NA, or with the value provided in the FILLVALUE argument.
If BIMETS_CONF_CCT='XTS', in the case of a monthly input time series the .indexCLASS is converted to the class yearmon(); in the case of a quarterly input time series the .indexCLASS is converted to yearqtr(); in the case of other input frequency the .indexCLASS is converted to Date(). If BIMETS_CONF_CCT='XTS' the dates of all the output observations are set accordingly to the BIMETS global option BIMETS_CONF_DIP, i.e. the first or the last dates in the period (see BIMETS configuration).
If the input time series has multiple observations in the same date, e.g. an xts() with a two or more observations in the same date, the duplication is removed and the output time series will contain only the later observation (see example).
If the input time series is multivariate, the output time series will contain only the first column of the input matrix of data (where the matrix of data is the matrix built by binding input time series values as columns).
If the input time series is a daily time series of class xts() and the global option BIMETS_CONF_CCT='TS' then the 366th period of the output time series in each non-bissextile year will have the value of the 365th period in the same year (duplicated value).
as.bimets(x=NULL, FILLVALUE=NA, VERBOSE=FALSE, ...)as.bimets(x=NULL, FILLVALUE=NA, VERBOSE=FALSE, ...)
x |
Input time series of class |
FILLVALUE |
Value inserted in the output time series in the case of temporal discontinuity. Defaults to missing NA. |
VERBOSE |
If |
... |
Backward compatibility. |
This function returns a BIMETS time series (see also BIMETS configuration)
.
is.bimetsTIMESERIESBIMETS indexingBIMETS configurationfromBIMETStoXTSfromBIMETStoTS
#xts series with dates equal to the first date in the period, #and some missing observations #first...set option and work with xts setBIMETSconf('BIMETS_CONF_CCT','XTS') #create xts xt<-xts(1:10,order.by=seq(as.Date('2000-01-01'),len=10,by='year')) #remove some data xt<-xt[-5] xt<-xt[-3] #convert to bimets xtBimets<-as.bimets(xt) #print before and after... print(xt) print(xtBimets) #ts bivariate series into xts setBIMETSconf('BIMETS_CONF_CCT','XTS') ts<-ts(matrix(c(1,2,3,4,5,6),nrow=3,ncol=2),start=c(2000,1),frequency=1) print(ts) xtsBimets<-as.bimets(ts) print(xtsBimets) #reset defaults setBIMETSconf('BIMETS_CONF_DIP','LAST') setBIMETSconf('BIMETS_CONF_CCT','TS') #xts quarterly with irregular dates and missings data xt<-xts(1:10,order.by=seq(as.Date('2000-01-03'),len=10,by='3 months')) #remove some data xt<-xt[-5] xt<-xt[-3] #convert tsBimets<-as.bimets(xt) #print before and after print(xt) print(tsBimets) #xts daily with duplicated observations and missing data xt<-xts(1:11,order.by=c(as.Date('2000-01-01'), seq(as.Date('2000-01-01'), len=10,by='day'))) xt<-xt[-5] xt<-xt[-3] #convert tsBimets<-as.bimets(xt) #print before and after print(xt) print(tsBimets) #verbose and fillvalue xt<-xts(1:11,order.by=c(as.Date('2000-01-01'), seq(as.Date('2000-01-01'), len=10,by='day'))) xt<-xt[-5] xt<-xt[-3] as.bimets(xt,FILLVALUE=99.99,VERBOSE=TRUE)#xts series with dates equal to the first date in the period, #and some missing observations #first...set option and work with xts setBIMETSconf('BIMETS_CONF_CCT','XTS') #create xts xt<-xts(1:10,order.by=seq(as.Date('2000-01-01'),len=10,by='year')) #remove some data xt<-xt[-5] xt<-xt[-3] #convert to bimets xtBimets<-as.bimets(xt) #print before and after... print(xt) print(xtBimets) #ts bivariate series into xts setBIMETSconf('BIMETS_CONF_CCT','XTS') ts<-ts(matrix(c(1,2,3,4,5,6),nrow=3,ncol=2),start=c(2000,1),frequency=1) print(ts) xtsBimets<-as.bimets(ts) print(xtsBimets) #reset defaults setBIMETSconf('BIMETS_CONF_DIP','LAST') setBIMETSconf('BIMETS_CONF_CCT','TS') #xts quarterly with irregular dates and missings data xt<-xts(1:10,order.by=seq(as.Date('2000-01-03'),len=10,by='3 months')) #remove some data xt<-xt[-5] xt<-xt[-3] #convert tsBimets<-as.bimets(xt) #print before and after print(xt) print(tsBimets) #xts daily with duplicated observations and missing data xt<-xts(1:11,order.by=c(as.Date('2000-01-01'), seq(as.Date('2000-01-01'), len=10,by='day'))) xt<-xt[-5] xt<-xt[-3] #convert tsBimets<-as.bimets(xt) #print before and after print(xt) print(tsBimets) #verbose and fillvalue xt<-xts(1:11,order.by=c(as.Date('2000-01-01'), seq(as.Date('2000-01-01'), len=10,by='day'))) xt<-xt[-5] xt<-xt[-3] as.bimets(xt,FILLVALUE=99.99,VERBOSE=TRUE)
BIMETS package depends on some options in order to transform and to present time series data. These options can be read or changed by using the functions:setBIMETSconf(opt,value) and getBIMETSconf(opt)
setBIMETSconf(opt=NULL, value=NULL, suppressOutput=FALSE) getBIMETSconf(opt=NULL)setBIMETSconf(opt=NULL, value=NULL, suppressOutput=FALSE) getBIMETSconf(opt=NULL)
opt |
Name of the BIMETS option. Available option names are: |
value |
The value to be assigned to the BIMETS option. |
suppressOutput |
If |
This function set or read global BIMETS options, and return a NULL value.
TIMESERIESis.bimetsas.bimetsfromBIMETStoXTSfromBIMETStoTSBIMETS indexing
#default BIMETS_CONF_DIP is LAST #create ts ts1<-TSERIES((1:10),START=c(2000,1),FREQ=1) #transform to xts and print xt1<-fromBIMETStoXTS(ts1) print(xt1) #....dates as of 31 Dec #set configuration BIMETS_CONF_DIP to FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') #create ts ts1<-TSERIES((1:10),START=c(2000,1),FREQ=1) #transform to xts and print xt1<-fromBIMETStoXTS(ts1) print(xt1) #....dates as of 1 Jan #set configuration BIMETS_CONF_DIP to LAST setBIMETSconf('BIMETS_CONF_DIP','LAST') #default to XTS setBIMETSconf('BIMETS_CONF_CCT','XTS') #check compliance of xt1 and fail... is.bimets(xt1) #... FALSE #set configuration BIMETS_CONF_DIP to FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') #check compliance of xt1 and ok... is.bimets(xt1) #... TRUE print(getBIMETSconf('BIMETS_CONF_DIP')) # ... returns FIRST print(getBIMETSconf('BIMETS_CONF_CCT')) # ... returns XTS print(is.xts(TSERIES(1:10,START=c(2000,1),FREQ=1))) #...print TRUE print(is.ts(TSERIES(1:10,START=c(2000,1),FREQ=1,class='TS'))) #...print TRUE #NOC setBIMETSconf('BIMETS_CONF_CCT','XTS') is.bimets(xts()) #FALSE setBIMETSconf('BIMETS_CONF_NOC',TRUE) is.bimets(xts()) #TRUE #...back to defaults setBIMETSconf('BIMETS_CONF_DIP','LAST') setBIMETSconf('BIMETS_CONF_CCT','TS') setBIMETSconf('BIMETS_CONF_NOC',FALSE)#default BIMETS_CONF_DIP is LAST #create ts ts1<-TSERIES((1:10),START=c(2000,1),FREQ=1) #transform to xts and print xt1<-fromBIMETStoXTS(ts1) print(xt1) #....dates as of 31 Dec #set configuration BIMETS_CONF_DIP to FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') #create ts ts1<-TSERIES((1:10),START=c(2000,1),FREQ=1) #transform to xts and print xt1<-fromBIMETStoXTS(ts1) print(xt1) #....dates as of 1 Jan #set configuration BIMETS_CONF_DIP to LAST setBIMETSconf('BIMETS_CONF_DIP','LAST') #default to XTS setBIMETSconf('BIMETS_CONF_CCT','XTS') #check compliance of xt1 and fail... is.bimets(xt1) #... FALSE #set configuration BIMETS_CONF_DIP to FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') #check compliance of xt1 and ok... is.bimets(xt1) #... TRUE print(getBIMETSconf('BIMETS_CONF_DIP')) # ... returns FIRST print(getBIMETSconf('BIMETS_CONF_CCT')) # ... returns XTS print(is.xts(TSERIES(1:10,START=c(2000,1),FREQ=1))) #...print TRUE print(is.ts(TSERIES(1:10,START=c(2000,1),FREQ=1,class='TS'))) #...print TRUE #NOC setBIMETSconf('BIMETS_CONF_CCT','XTS') is.bimets(xts()) #FALSE setBIMETSconf('BIMETS_CONF_NOC',TRUE) is.bimets(xts()) #TRUE #...back to defaults setBIMETSconf('BIMETS_CONF_DIP','LAST') setBIMETSconf('BIMETS_CONF_CCT','TS') setBIMETSconf('BIMETS_CONF_NOC',FALSE)
BIMETS package contains example datasets in order to execute code in vignettes, and hidden technical datasets in order to allow a faster performance in time series analysis.
TIMESERIESis.bimetsas.bimetsfromBIMETStoXTSfromBIMETStoTSBIMETS indexing
This function returns the cumulative product of the elements of the input array or time series. The result is an object of the same class of the input, and its elements are the cumulative product of the current and the previous elements of the input.
If the input is a time series, users can provide the argument TSRANGE in order to project the input time series before the cumulative product.
CUMPROD(x=NULL, TSRANGE=NULL, ignoreNA=FALSE, avoidCompliance=FALSE, ...)CUMPROD(x=NULL, TSRANGE=NULL, ignoreNA=FALSE, avoidCompliance=FALSE, ...)
x |
Input numerical array or time series that must satisfy the compliance control check defined in |
TSRANGE |
Optional date range of operations that process the input time series. |
ignoreNA |
Ignore missing values. |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns an object of the same class of the input, i.e. an array or a BIMETS time series.
TSPROJECTMOVAVGTSDELTATSLAGTSPROJECTTSEXTENDTSLEADINDEXNUMVERIFY_MAGNITUDE
#create ts ts1<-TSERIES(INTS(1,10),START=c(2000,1),FREQ='M') out_CUMPROD<-CUMPROD(ts1) TABIT(out_CUMPROD) out_CUMPROD<-CUMPROD(ts1,TSRANGE=c(2000,4,2001,1)) TABIT(ts1,out_CUMPROD) #define an array arr1<-c(INTS(1,5),INTS(-1,-5)) out_CUMPROD<-CUMPROD(arr1) print(out_CUMPROD)#create ts ts1<-TSERIES(INTS(1,10),START=c(2000,1),FREQ='M') out_CUMPROD<-CUMPROD(ts1) TABIT(out_CUMPROD) out_CUMPROD<-CUMPROD(ts1,TSRANGE=c(2000,4,2001,1)) TABIT(ts1,out_CUMPROD) #define an array arr1<-c(INTS(1,5),INTS(-1,-5)) out_CUMPROD<-CUMPROD(arr1) print(out_CUMPROD)
This function returns the cumulative sum of the elements of the input array or time series. The result is an object of the same class of the input, and its elements are the cumulative sum of the current and the previous elements of the input.
If the input is a time series, users can provide the argument TSRANGE in order to project the input time series before the cumulative sum. CUMULO is an alias form CUMSUM with the argument MODE='YEARLY'.
CUMSUM(x=NULL, TSRANGE=NULL, MODE=NULL, ignoreNA=FALSE, avoidCompliance=FALSE,...) CUMULO(x=NULL, TSRANGE=NULL, ignoreNA=FALSE, avoidCompliance=FALSE,...)CUMSUM(x=NULL, TSRANGE=NULL, MODE=NULL, ignoreNA=FALSE, avoidCompliance=FALSE,...) CUMULO(x=NULL, TSRANGE=NULL, ignoreNA=FALSE, avoidCompliance=FALSE,...)
x |
Input numerical array or time series that must satisfy the compliance control check defined in |
TSRANGE |
Optional date range of operations that process time series. |
MODE |
When selecting |
ignoreNA |
Ignore missing values. |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns an object of the same class of the input, i.e. an array or a BIMETS time series.
TSPROJECTMOVAVGTSDELTATSLAGTSPROJECTTSEXTENDTSLEADINDEXNUMCUMPRODVERIFY_MAGNITUDEGETRANGE
#create ts ts1<-TSERIES(INTS(1,30),START=c(2000,1),FREQ='M') out_CUMSUM<-CUMSUM(ts1) TABIT(out_CUMSUM) out_CUMSUM<-CUMSUM(ts1,TSRANGE=c(2000,4,2001,7)) out_CUMSUM_Y<-CUMSUM(ts1,TSRANGE=c(2000,4,2001,7),MODE='YEARLY') TABIT(ts1,out_CUMSUM,out_CUMSUM_Y) #define an array arr1<-c(INTS(1,10),INTS(-1,-10)) out_CUMSUM<-CUMSUM(arr1) print(out_CUMSUM) #print...1 3 6 10 15 21 ... 27 19 10 0#create ts ts1<-TSERIES(INTS(1,30),START=c(2000,1),FREQ='M') out_CUMSUM<-CUMSUM(ts1) TABIT(out_CUMSUM) out_CUMSUM<-CUMSUM(ts1,TSRANGE=c(2000,4,2001,7)) out_CUMSUM_Y<-CUMSUM(ts1,TSRANGE=c(2000,4,2001,7),MODE='YEARLY') TABIT(ts1,out_CUMSUM,out_CUMSUM_Y) #define an array arr1<-c(INTS(1,10),INTS(-1,-10)) out_CUMSUM<-CUMSUM(arr1) print(out_CUMSUM) #print...1 3 6 10 15 21 ... 27 19 10 0
This function returns a daily disaggregated time series, by using as input an annual, semiannual, quarterly or monthly time series.
DAILY(x = NULL, fun = NULL, avoidCompliance = FALSE, ...)DAILY(x = NULL, fun = NULL, avoidCompliance = FALSE, ...)
x |
Input time series, that must satisfy the compliance control check defined in |
fun |
NULL: (default) the output value of each daily observation is set equal to the value of the input observation the date belongs to (i.e. duplicated values over the period) |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a daily BIMETS time series.
YEARLYSEMIANNUALQUARTERLYMONTHLY
#TS quarterly ts1<-TSERIES((1:2),START=c(2000,1),FREQ='Q') TABIT(DAILY(ts1,fun='INTERP_CENTER')) #TS monthly ts1<-TSERIES((1:4),START=c(2000,1),FREQ=12) TABIT(DAILY(ts1))#TS quarterly ts1<-TSERIES((1:2),START=c(2000,1),FREQ='Q') TABIT(DAILY(ts1,fun='INTERP_CENTER')) #TS monthly ts1<-TSERIES((1:4),START=c(2000,1),FREQ=12) TABIT(DAILY(ts1))
This function converts an object of class Date() to an array c(YEAR,PERIOD), where YEAR and PERIOD are the year-period the input Date() belongs to, given an input frequency.
date2yp(x = NULL, f = 1)date2yp(x = NULL, f = 1)
x |
Input of class |
f |
Positive integer. Valid values are: 1, 2, 3, 4, 12, 24, 36, 53, 366 |
This function returns a two-dimensional array c(YEAR,PERIOD).
print(date2yp(as.Date('2001/06/30'),2)) #2001,1 print(date2yp(as.Date('2002/03/23'),1)) #2002,1 print(date2yp(as.Date('2003/07/01'),366)) #2003,182 print(date2yp(as.Date('2004/09/13'),2)) #2004,2 print(date2yp(as.Date('2004/01/13'),12)) #2004,1 print(date2yp(as.Date('2004/07/24'),4)) #2004,3 print(date2yp(c(as.Date('1900-01-01'),as.Date('1944-12-01'), as.Date('1964-06-12'),as.Date('1923-03-01'), as.Date('1943-12-05')),f=366)) #...print(date2yp(as.Date('2001/06/30'),2)) #2001,1 print(date2yp(as.Date('2002/03/23'),1)) #2002,1 print(date2yp(as.Date('2003/07/01'),366)) #2003,182 print(date2yp(as.Date('2004/09/13'),2)) #2004,2 print(date2yp(as.Date('2004/01/13'),12)) #2004,1 print(date2yp(as.Date('2004/07/24'),4)) #2004,3 print(date2yp(c(as.Date('1900-01-01'),as.Date('1944-12-01'), as.Date('1964-06-12'),as.Date('1923-03-01'), as.Date('1943-12-05')),f=366)) #...
This function eliminates the selected elements from the input array or the input time series.
ELIMELS(x=NULL, idx=NULL, avoidCompliance=FALSE, ...)ELIMELS(x=NULL, idx=NULL, avoidCompliance=FALSE, ...)
x |
Input numerical array or time series that must satisfy the compliance control check defined in |
idx |
Numerical array built with the indices of selected elements to be removed from the input. If the input is a time series the index must be provided as a sequence of numbers |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns an array with the kept elements from the input array or the input time series.
TIMESERIESis.bimetsBIMETS indexingGETYEARPERIODLOCSNAMELISTINTSTSINFOTSLOOKTABITNOELS
print(ELIMELS(INTS(1,10),c(1,4,5))) #print 2 3 6 7 8 9 10 print(ELIMELS(TSERIES(1:10,START=c(2000,1),FREQ=4),c(2000.25,2000.75))) #print 2 4 5 6 7 8 9 10print(ELIMELS(INTS(1,10),c(1,4,5))) #print 2 3 6 7 8 9 10 print(ELIMELS(TSERIES(1:10,START=c(2000,1),FREQ=4),c(2000.25,2000.75))) #print 2 4 5 6 7 8 9 10
This function estimates equations that are linear in the coefficients, as specified in the behavioral equations of the input model object. Coefficients can be estimated for single equations or blocks of simultaneous equations. Coefficients restriction procedure derives from Lagrange Multipliers' theory, while the Cochrane-Orcutt method allows accounting for residuals autocorrelation.
The estimation function supports:
- Ordinary Least Squares;
- Instrumental Variables;
- Deterministic linear restrictions on the coefficients;
- Almon Polynomial Distributed Lags;
- Autocorrelation of the errors;
- Structural stability analysis (Chow tests);
Further details on estimation calculus can be found in MDL help page; further details on Chow test can be found below in this section;
ESTIMATE(model=NULL, eqList=NULL, TSRANGE=NULL, forceTSRANGE=FALSE, estTech='OLS', IV=NULL, forceIV=FALSE, quietly=FALSE, tol=1e-28, digits=getOption('digits'), centerCOV=TRUE, CHOWTEST=FALSE, CHOWPAR=NULL, avoidCompliance=FALSE, ...)ESTIMATE(model=NULL, eqList=NULL, TSRANGE=NULL, forceTSRANGE=FALSE, estTech='OLS', IV=NULL, forceIV=FALSE, quietly=FALSE, tol=1e-28, digits=getOption('digits'), centerCOV=TRUE, CHOWTEST=FALSE, CHOWPAR=NULL, avoidCompliance=FALSE, ...)
model |
The BIMETS model object to be estimated (see also |
eqList |
The |
TSRANGE |
The time range of the estimation, as a four dimensional numerical array, |
forceTSRANGE |
If |
estTech |
The estimation technique used in the regression. Ordinary Least Squares |
IV |
The |
forceIV |
If |
quietly |
If |
tol |
The tolerance for detecting linear dependencies in a matrix's columns when its inverse is requested. |
digits |
Controls the number of digits to print when printing coefficients and statistics of the estimation. Valid values are 1 to 22 with a default of 7. |
centerCOV |
If |
CHOWTEST |
If |
CHOWPAR |
Indicates the last year-period where the stability test is performed. If |
avoidCompliance |
If |
... |
Backward compatibility. |
If outputText=TRUE, for each behavioral in the eqList this function will print out:
- the name of the estimated behavioral;
- the estimation technique used;
- the autocorrelation order of the error, if any, and the iterations count required to achieve the convergence;
- the estimated equation with calculated coefficients and regressor expression; for each coefficient the T-statistic and the significance will be printed out;
- the restriction equations imposed on the coefficients, if any;
- the F-test for the restrictions, including the PDL restrictions, if any;
- the final autocorrelation parameters for the error, along with their standard error, the T-statistic and the significance;
- the R-Squared and the Adjusted R-Squared;
- the Durbin-Watson Statistic;
- the Sum of squares of residuals;
- the Standard Error of Regression;
- the Log of the Likelihood Function;
- the F-statistic and the F-probability;
- the AIC and the BIC;
- the Mean of the Dependent Variable;
- the Number of Observations;
- the Number of Degrees of Freedom;
- the Current Sample, i.e. the TSRANGE of estimation;
All probabilities lie between [0, 1].
For each behavioral in the eqList this function will add 4 new named elements into the related behavioral of the output model object:
1) coefficients: a numerical array built with the estimated coefficients;
2) errorCoefficients: a numerical array built with the estimated coefficient for the error autoregression, if the ERROR> structure has been provided in the model MDL definition;
3) residuals: the time series of the regression residuals. If an ERROR> structure has been provided in the behavioral definition, the related residuals will be calculated as described in the Cochrane-Orcutt procedure (see MDL).
3) residuals_no_error_correction: if an ERROR> structure has been provided in the behavioral definition, the residuals calcucated by using the original dependent and independent variables are stored into this list element.
4) statistics: a list built with the parameters and the statistics of the estimation, e.g.:
- TSRANGE: TSRANGE requested in the latest estimation of the behavioral;
- estimationTechinque: estimation technique requested in the latest estimation of the behavioral;
- CoeffCovariance: coefficients covariance;
- StandardErrorRegression and StandardErrorRegressionNotCentered: standard error of the regression (centered and not-centered);
- CoeffTstatistic: T-statistic of the coefficients;
- RSquared: R-Squared;
- AdjustedRSquared: adjusted R-Squared;
- DegreesOfFreedom: degrees of freedom of the regression;
- CoeffPvalues: coefficients p-values;
- LogLikelihood: Log of the Likelihood Function;
- Fstatistics: F-statistics;
- RhosTstatistics: rhos T-statistic (if any);
- FtestRestrValue: F-test value for the restrictions;
- FtestRestrProbability: F-test probability for the restrictions;
- AIC: Akaike's Information Criterion;
- BIC: Schwarz's Information Criterion;
- matrixX: the regressors matrix;
- vectorY: the dependent variable;
- matrixX_error_corrected: the regressors matrix arising from the Cochrane-Orcutt procedure;
- etc.
Structural Stability - Chow test
One of the main purposes of econometric modeling is its use for forecast and policy evaluation and, to this end, the stability of any behavioral equation parameters over time should be verified. In order to check for structural stability two different procedures, which can be derived from the so-called Chow-tests, are applied.
Given a sample of observations (i.e. the base TSRANGE) and selecting an arbitrary forward extension in observations (i.e. the extended TSRANGE), with , in the general case we have the following two regressions:
1) , having time series projected on the base TSRANGE
2) , having time series projected on the extended TSRANGE
In general, a stability analysis is carried on in the following ways:
- comparing the parameter estimates arising from the two regressions: this is known as the covariance analysis;
- checking the accuracy of the forecast for the dependent variable in the extended TSRANGE, using the estimates produced in the base TSRANGE: this is known as the predictive power test.
The first Chow test is calculated as:
,
with as the sum of squared residuals and as the number of degrees of freedom in the regression .
The test is completed by calculating the following time series on the extended TSRANGE:
- the forecast error;
- the standard error of forecast;
- the t-statistic for the error;
The standard error of the forecast for the observation in the extended TSRANGE is computed according to:
having as the independent values (i.e. regressors) on the observation in the extended TSRANGE, with .
The null hypothesis for is: , given
The test statistic follows the distribution with and degrees of freedom, and can be performed during the ESTIMATE() function execution by using the CHOWTEST argument set to TRUE.
If CHOWTEST is TRUE, for each behavioral in the eqList the output model will have the following named element:
- ChowTest: it contains the statistics and the time series computed during the last structural analysis performed on the related behavioral.
MDLLOAD_MODELSIMULATESTOCHSIMULATEMULTMATRIXRENORMOPTIMIZETIMESERIESBIMETS indexingBIMETS configurationsummary
#define model myModelDefinition<- "MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions COMMENT> and conditional evaluations COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment BEHAVIORAL> i TSRANGE 1923 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model myModel<-LOAD_MODEL(modelText=myModelDefinition) #load data into the model myModel<-LOAD_MODEL_DATA(myModel,myModelData,showWarnings = TRUE) ################################################# #OLS case #estimate the model myModel<-ESTIMATE(myModel) #HERE BELOW THE OUTPUT OF THE ESTIMATION (COMMENTED OUT): #.CHECK_MODEL_DATA(): warning, there are undefined values in time series "time". # #Estimate the Model myModelDefinition: #the number of behavioral equations to be estimated is 3. #The total number of coefficients is 14. # #_________________________________________ # #BEHAVIORAL EQUATION: cn #Estimation Technique: OLS #Autoregression of Order 2 (Cochrane-Orcutt procedure) # #Convergence was reached in 9 / 20 iterations. # # #cn = 19.01352 # T-stat. 12.13083 *** # # + 0.3442816 p # T-stat. 3.533253 ** # # + 0.03443117 TSLAG(p,1) # T-stat. 0.3937881 # # + 0.6993905 (w1+w2) # T-stat. 14.0808 *** # #ERROR STRUCTURE: AUTO(2) # #AUTOREGRESSIVE PARAMETERS: #Rho Std. Error T-stat. # 0.05743131 0.3324101 0.1727725 # 0.007785936 0.2647013 0.02941404 # # #STATs: #R-Squared : 0.985263 #Adjusted R-Squared : 0.9785644 #Durbin-Watson Statistic : 1.966609 #Sum of squares of residuals : 9.273455 #Standard Error of Regression : 0.9181728 #Log of the Likelihood Function : -18.97047 #F-statistic : 147.0844 #F-probability : 1.090551e-09 #Akaike's IC : 51.94093 #Schwarz's IC : 57.77343 #Mean of Dependent Variable : 55.71765 #Number of Observations : 17 #Number of Degrees of Freedom : 11 #Current Sample (year-period) : 1925-1 / 1941-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # # #_________________________________________ # #BEHAVIORAL EQUATION: i #Estimation Technique: OLS # #i = 2.868104 # T-stat. 0.3265098 # # + 0.5787626 p # T-stat. 4.456542 *** # # + 0.4212374 TSLAG(p,1) # T-stat. 3.243579 ** # # - 0.09160307 TSLAG(k,1) # T-stat. -2.11748 # #RESTRICTIONS: #b2+b3=1 # #RESTRICTIONS F-TEST: #F-value : 8.194478 #F-prob(1,15) : 0.0118602 # # #STATs: #R-Squared : 0.8928283 #Adjusted R-Squared : 0.8794319 #Durbin-Watson Statistic : 1.173106 #Sum of squares of residuals : 26.76483 #Standard Error of Regression : 1.293368 #Log of the Likelihood Function : -30.215 #F-statistic : 66.64659 #F-probability : 1.740364e-08 #Akaike's IC : 68.43001 #Schwarz's IC : 72.20776 #Mean of Dependent Variable : 1.310526 #Number of Observations : 19 #Number of Degrees of Freedom : 16 #Current Sample (year-period) : 1923-1 / 1941-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # # #_________________________________________ # #BEHAVIORAL EQUATION: w1 #Estimation Technique: OLS # #w1 = 1.12869 # T-stat. 0.6479266 # # + 0.4398767 (y+t-w2) # T-stat. 12.01268 *** # # + c3 TSLAG(y+t-w2,1) # PDL # # + 0.1368206 time # T-stat. 3.373905 ** # #PDL: #c3 1 3 # #Distributed Lag Coefficient: c3 #Lag Coeff. Std. Error T-stat. #0 0.1076812 0.04283967 2.513586 * #1 0.05074557 0.01291231 3.930015 ** #2 -0.00619005 0.03110492 -0.1990055 #SUM 0.1522367 0.03873693 # #RESTRICTIONS F-TEST: #F-value : 0.06920179 #F-prob(1,11) : 0.7973647 # # #STATs: #R-Squared : 0.9890855 #Adjusted R-Squared : 0.9854474 #Durbin-Watson Statistic : 2.174168 #Sum of squares of residuals : 6.392707 #Standard Error of Regression : 0.7298805 #Log of the Likelihood Function : -15.80848 #F-statistic : 271.8645 #F-probability : 1.172284e-11 #Akaike's IC : 43.61697 #Schwarz's IC : 48.61625 #Mean of Dependent Variable : 37.69412 #Number of Observations : 17 #Number of Degrees of Freedom : 12 #Current Sample (year-period) : 1925-1 / 1941-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # #...ESTIMATE OK #get residuals of 'cn' myModel$behaviorals$cn$residuals #Time Series: #Start = 1925 #End = 1941 #Frequency = 1 # [1] -0.88562504 0.25109884 0.66750111 ... #[17] -1.41795908 #get residuals of 'i' myModel$behaviorals$i$residuals #Time Series: #Start = 1923 #End = 1941 #Frequency = 1 # [1] 1.464518775 -1.469763968 0.078674017 ... #[16] -2.425079127 -0.698071507 -1.352967430 -1.724306054 #get estimation coefficients of 'cn' and 'w1' myModel$behaviorals$cn$coefficients # [,1] #a1 19.01352476 #a2 0.34428157 #a3 0.03443117 #a4 0.69939052 myModel$behaviorals$cn$errorCoefficients # [,1] #RHO_1 0.057431312 #RHO_2 0.007785936 myModel$behaviorals$w1$coefficients # [,1] #c1 1.12869024 #c2 0.43987666 #c3 0.10768118 #c3_PDL_1 0.05074557 #c3_PDL_2 -0.00619005 #c4 0.13682057 ################################################# #IV case #estimation of Consumption "cn" with arbitrary IVs #and error autocorrelation myModel<-ESTIMATE(myModel, eqList = 'cn', estTech = 'IV', IV=c('1', 'TSLAG(y)', 'TSLAG(w1)*pi+0.5', 'exp(w2)')) #Estimate the Model myModelDefinition: #the number of behavioral equations to be estimated is 1. #The total number of coefficients is 4. # #_________________________________________ # #BEHAVIORAL EQUATION: cn #Estimation Technique: IV #Autoregression of Order 2 (Cochrane-Orcutt procedure) # #Convergence was reached in 7 / 20 iterations. # # #cn = 18.07073 # T-stat. 11.72958 *** # # + 0.2530483 p # T-stat. 1.583881 # # + 0.08631646 TSLAG(p,1) # T-stat. 0.7556204 # # + 0.7363227 (w1+w2) # T-stat. 13.11572 *** # #ERROR STRUCTURE: AUTO(2) # #AUTOREGRESSIVE PARAMETERS: #Rho Std. Error T-stat. #0.01559806 0.343195 0.04544955 #-0.1196327 0.283432 -0.422086 # # #STATs: #R-Squared : 0.9843186 #Adjusted R-Squared : 0.9771907 #Durbin-Watson Statistic : 1.917329 #Sum of squares of residuals : 9.867739 #Standard Error of Regression : 0.9471363 #Log of the Likelihood Function : -19.49844 #F-statistic : 138.0938 #F-probability : 1.532807e-09 #Akaike's IC : 52.99689 #Schwarz's IC : 58.82938 #Mean of Dependent Variable : 55.71765 #Number of Observations : 17 #Number of Degrees of Freedom : 11 #Current Sample (year-period) : 1925-1 / 1941-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # #...ESTIMATE OK #define model myShortModelDefinition<- "MODEL COMMENT> Consumption with IV BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 IV> 1 IV> TSLAG(y) IV> TSLAG(w1)*pi+0.5 IV> exp(w2) END " #load model myShortModel<-LOAD_MODEL(modelText=myShortModelDefinition) #load data into the model myShortModel<-LOAD_MODEL_DATA(myShortModel,myModelData,showWarnings = TRUE) #estimation of Consumption "cn" with arbitrary IVs #and error autocorrelation myShortModel<-ESTIMATE(myShortModel, eqList = 'cn', estTech = 'IV') #estimation of Investment "i" with arbitrary IVs #and coefficient restrictions myModel<-ESTIMATE(myModel, eqList = 'i', estTech = 'IV', IV=c('1', 'TSLAG(w2)', 'TSLAG(w1)*pi+0.5', 'exp(w2)')) #.CHECK_MODEL_DATA(): warning, there are undefined values in time series "time". # #Estimate the Model myModelDefinition: #the number of behavioral equations to be estimated is 1. #The total number of coefficients is 4. # #_________________________________________ # #BEHAVIORAL EQUATION: i #Estimation Technique: IV # #i = 34.517544 # T-stat. 1.264388 # # + 0.3216326 p # T-stat. 0.8648297 # # + 0.6783672 TSLAG(p,1) # T-stat. 1.824043 # # - 0.2475568 TSLAG(k,1) # T-stat. -1.842520 # #RESTRICTIONS: #b2+b3=1 # #RESTRICTIONS F-TEST: #F-value : 2.465920 #F-prob(1,15) : 0.137190 # # #STATs: #R-Squared : 0.805773 #Adjusted R-Squared : 0.781494 #Durbin-Watson Statistic : 0.940534 #Sum of squares of residuals : 48.50580 #Standard Error of Regression : 1.741152 #Log of the Likelihood Function : -35.86365 #F-statistic : 33.18894 #F-probability : 2.025229e-06 #Akaike's IC : 79.72731 #Schwarz's IC : 83.50506 #Mean of Dependent Variable : 1.310526 #Number of Observations : 19 #Number of Degrees of Freedom : 16 #Current Sample (year-period) : 1923-1 / 1941-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # #...ESTIMATE OK ############################################################## #CHOW TEST on w1 #base TSRANGE set to 1925 / 1935 myModel<-ESTIMATE(myModel, eqList='w1', TSRANGE=c(1925,1,1935,1), forceTSRANGE=TRUE, CHOWTEST=TRUE) #Estimate the Model myModelDefinition: #the number of behavioral equations to be estimated is 1. #The total number of coefficients is 6. # #_________________________________________ # #BEHAVIORAL EQUATION: w1 #Estimation Technique: OLS # #w1 = - 4.48873 # T-stat. -2.47402 * # # + 0.545102 (y+t-w2) # T-stat. 15.3462 *** # # + c3 TSLAG(y+t-w2,1) # PDL # # + 0.292018 time # T-stat. 5.58588 ** # #PDL: #c3 1 3 # #Distributed Lag Coefficient: c3 #Lag Coeff. Std. Error T-stat. #0 0.0413985 0.0336676 1.22963 #1 0.0493551 0.00742323 6.64873 *** #2 0.0573116 0.0265487 2.15873 #SUM 0.148065 0.0222697 # #RESTRICTIONS F-TEST: #F-value : 3.35954 #F-prob(1,5) : 0.126295 # # #STATs: #R-Squared : 0.995931 #Adjusted R-Squared : 0.993219 #Durbin-Watson Statistic : 2.43313 #Sum of squares of residuals : 0.737093 #Standard Error of Regression : 0.350498 #Log of the Likelihood Function : -0.742173 #F-statistic : 367.183 #F-probability : 2.68564e-07 #Akaike's IC : 13.4843 #Schwarz's IC : 15.8717 #Mean of Dependent Variable : 34.9909 #Number of Observations : 11 #Number of Degrees of Freedom : 6 #Current Sample (year-period) : 1925-1 / 1935-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # # #STABILITY ANALYSIS: #Behavioral equation: w1 # #Chow test: #Sample (auto) : 1936-1 / 1941-1 #F-value : 15.3457 #F-prob(6,12) : 5.34447e-05 # #Predictive Power: # #Date, Prd., Actual , Predict , Error , Std. Error , T-stat # #1936, 1 , 36.8 , 38.439 , -1.63901 , 0.547471 , -2.99378 #1937, 1 , 41 , 40.824 , 0.176033 , 0.630905 , 0.279017 #1938, 1 , 38.2 , 39.6553 , -1.4553 , 0.672192 , -2.165 #1939, 1 , 41.6 , 45.0547 , -3.45466 , 0.834433 , -4.14012 #1940, 1 , 45 , 49.0118 , -4.01179 , 0.966472 , -4.15096 #1941, 1 , 53.3 , 56.6727 , -3.37275 , 1.23486 , -2.73127 # # #...ESTIMATE OK#define model myModelDefinition<- "MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions COMMENT> and conditional evaluations COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment BEHAVIORAL> i TSRANGE 1923 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model myModel<-LOAD_MODEL(modelText=myModelDefinition) #load data into the model myModel<-LOAD_MODEL_DATA(myModel,myModelData,showWarnings = TRUE) ################################################# #OLS case #estimate the model myModel<-ESTIMATE(myModel) #HERE BELOW THE OUTPUT OF THE ESTIMATION (COMMENTED OUT): #.CHECK_MODEL_DATA(): warning, there are undefined values in time series "time". # #Estimate the Model myModelDefinition: #the number of behavioral equations to be estimated is 3. #The total number of coefficients is 14. # #_________________________________________ # #BEHAVIORAL EQUATION: cn #Estimation Technique: OLS #Autoregression of Order 2 (Cochrane-Orcutt procedure) # #Convergence was reached in 9 / 20 iterations. # # #cn = 19.01352 # T-stat. 12.13083 *** # # + 0.3442816 p # T-stat. 3.533253 ** # # + 0.03443117 TSLAG(p,1) # T-stat. 0.3937881 # # + 0.6993905 (w1+w2) # T-stat. 14.0808 *** # #ERROR STRUCTURE: AUTO(2) # #AUTOREGRESSIVE PARAMETERS: #Rho Std. Error T-stat. # 0.05743131 0.3324101 0.1727725 # 0.007785936 0.2647013 0.02941404 # # #STATs: #R-Squared : 0.985263 #Adjusted R-Squared : 0.9785644 #Durbin-Watson Statistic : 1.966609 #Sum of squares of residuals : 9.273455 #Standard Error of Regression : 0.9181728 #Log of the Likelihood Function : -18.97047 #F-statistic : 147.0844 #F-probability : 1.090551e-09 #Akaike's IC : 51.94093 #Schwarz's IC : 57.77343 #Mean of Dependent Variable : 55.71765 #Number of Observations : 17 #Number of Degrees of Freedom : 11 #Current Sample (year-period) : 1925-1 / 1941-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # # #_________________________________________ # #BEHAVIORAL EQUATION: i #Estimation Technique: OLS # #i = 2.868104 # T-stat. 0.3265098 # # + 0.5787626 p # T-stat. 4.456542 *** # # + 0.4212374 TSLAG(p,1) # T-stat. 3.243579 ** # # - 0.09160307 TSLAG(k,1) # T-stat. -2.11748 # #RESTRICTIONS: #b2+b3=1 # #RESTRICTIONS F-TEST: #F-value : 8.194478 #F-prob(1,15) : 0.0118602 # # #STATs: #R-Squared : 0.8928283 #Adjusted R-Squared : 0.8794319 #Durbin-Watson Statistic : 1.173106 #Sum of squares of residuals : 26.76483 #Standard Error of Regression : 1.293368 #Log of the Likelihood Function : -30.215 #F-statistic : 66.64659 #F-probability : 1.740364e-08 #Akaike's IC : 68.43001 #Schwarz's IC : 72.20776 #Mean of Dependent Variable : 1.310526 #Number of Observations : 19 #Number of Degrees of Freedom : 16 #Current Sample (year-period) : 1923-1 / 1941-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # # #_________________________________________ # #BEHAVIORAL EQUATION: w1 #Estimation Technique: OLS # #w1 = 1.12869 # T-stat. 0.6479266 # # + 0.4398767 (y+t-w2) # T-stat. 12.01268 *** # # + c3 TSLAG(y+t-w2,1) # PDL # # + 0.1368206 time # T-stat. 3.373905 ** # #PDL: #c3 1 3 # #Distributed Lag Coefficient: c3 #Lag Coeff. Std. Error T-stat. #0 0.1076812 0.04283967 2.513586 * #1 0.05074557 0.01291231 3.930015 ** #2 -0.00619005 0.03110492 -0.1990055 #SUM 0.1522367 0.03873693 # #RESTRICTIONS F-TEST: #F-value : 0.06920179 #F-prob(1,11) : 0.7973647 # # #STATs: #R-Squared : 0.9890855 #Adjusted R-Squared : 0.9854474 #Durbin-Watson Statistic : 2.174168 #Sum of squares of residuals : 6.392707 #Standard Error of Regression : 0.7298805 #Log of the Likelihood Function : -15.80848 #F-statistic : 271.8645 #F-probability : 1.172284e-11 #Akaike's IC : 43.61697 #Schwarz's IC : 48.61625 #Mean of Dependent Variable : 37.69412 #Number of Observations : 17 #Number of Degrees of Freedom : 12 #Current Sample (year-period) : 1925-1 / 1941-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # #...ESTIMATE OK #get residuals of 'cn' myModel$behaviorals$cn$residuals #Time Series: #Start = 1925 #End = 1941 #Frequency = 1 # [1] -0.88562504 0.25109884 0.66750111 ... #[17] -1.41795908 #get residuals of 'i' myModel$behaviorals$i$residuals #Time Series: #Start = 1923 #End = 1941 #Frequency = 1 # [1] 1.464518775 -1.469763968 0.078674017 ... #[16] -2.425079127 -0.698071507 -1.352967430 -1.724306054 #get estimation coefficients of 'cn' and 'w1' myModel$behaviorals$cn$coefficients # [,1] #a1 19.01352476 #a2 0.34428157 #a3 0.03443117 #a4 0.69939052 myModel$behaviorals$cn$errorCoefficients # [,1] #RHO_1 0.057431312 #RHO_2 0.007785936 myModel$behaviorals$w1$coefficients # [,1] #c1 1.12869024 #c2 0.43987666 #c3 0.10768118 #c3_PDL_1 0.05074557 #c3_PDL_2 -0.00619005 #c4 0.13682057 ################################################# #IV case #estimation of Consumption "cn" with arbitrary IVs #and error autocorrelation myModel<-ESTIMATE(myModel, eqList = 'cn', estTech = 'IV', IV=c('1', 'TSLAG(y)', 'TSLAG(w1)*pi+0.5', 'exp(w2)')) #Estimate the Model myModelDefinition: #the number of behavioral equations to be estimated is 1. #The total number of coefficients is 4. # #_________________________________________ # #BEHAVIORAL EQUATION: cn #Estimation Technique: IV #Autoregression of Order 2 (Cochrane-Orcutt procedure) # #Convergence was reached in 7 / 20 iterations. # # #cn = 18.07073 # T-stat. 11.72958 *** # # + 0.2530483 p # T-stat. 1.583881 # # + 0.08631646 TSLAG(p,1) # T-stat. 0.7556204 # # + 0.7363227 (w1+w2) # T-stat. 13.11572 *** # #ERROR STRUCTURE: AUTO(2) # #AUTOREGRESSIVE PARAMETERS: #Rho Std. Error T-stat. #0.01559806 0.343195 0.04544955 #-0.1196327 0.283432 -0.422086 # # #STATs: #R-Squared : 0.9843186 #Adjusted R-Squared : 0.9771907 #Durbin-Watson Statistic : 1.917329 #Sum of squares of residuals : 9.867739 #Standard Error of Regression : 0.9471363 #Log of the Likelihood Function : -19.49844 #F-statistic : 138.0938 #F-probability : 1.532807e-09 #Akaike's IC : 52.99689 #Schwarz's IC : 58.82938 #Mean of Dependent Variable : 55.71765 #Number of Observations : 17 #Number of Degrees of Freedom : 11 #Current Sample (year-period) : 1925-1 / 1941-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # #...ESTIMATE OK #define model myShortModelDefinition<- "MODEL COMMENT> Consumption with IV BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 IV> 1 IV> TSLAG(y) IV> TSLAG(w1)*pi+0.5 IV> exp(w2) END " #load model myShortModel<-LOAD_MODEL(modelText=myShortModelDefinition) #load data into the model myShortModel<-LOAD_MODEL_DATA(myShortModel,myModelData,showWarnings = TRUE) #estimation of Consumption "cn" with arbitrary IVs #and error autocorrelation myShortModel<-ESTIMATE(myShortModel, eqList = 'cn', estTech = 'IV') #estimation of Investment "i" with arbitrary IVs #and coefficient restrictions myModel<-ESTIMATE(myModel, eqList = 'i', estTech = 'IV', IV=c('1', 'TSLAG(w2)', 'TSLAG(w1)*pi+0.5', 'exp(w2)')) #.CHECK_MODEL_DATA(): warning, there are undefined values in time series "time". # #Estimate the Model myModelDefinition: #the number of behavioral equations to be estimated is 1. #The total number of coefficients is 4. # #_________________________________________ # #BEHAVIORAL EQUATION: i #Estimation Technique: IV # #i = 34.517544 # T-stat. 1.264388 # # + 0.3216326 p # T-stat. 0.8648297 # # + 0.6783672 TSLAG(p,1) # T-stat. 1.824043 # # - 0.2475568 TSLAG(k,1) # T-stat. -1.842520 # #RESTRICTIONS: #b2+b3=1 # #RESTRICTIONS F-TEST: #F-value : 2.465920 #F-prob(1,15) : 0.137190 # # #STATs: #R-Squared : 0.805773 #Adjusted R-Squared : 0.781494 #Durbin-Watson Statistic : 0.940534 #Sum of squares of residuals : 48.50580 #Standard Error of Regression : 1.741152 #Log of the Likelihood Function : -35.86365 #F-statistic : 33.18894 #F-probability : 2.025229e-06 #Akaike's IC : 79.72731 #Schwarz's IC : 83.50506 #Mean of Dependent Variable : 1.310526 #Number of Observations : 19 #Number of Degrees of Freedom : 16 #Current Sample (year-period) : 1923-1 / 1941-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # #...ESTIMATE OK ############################################################## #CHOW TEST on w1 #base TSRANGE set to 1925 / 1935 myModel<-ESTIMATE(myModel, eqList='w1', TSRANGE=c(1925,1,1935,1), forceTSRANGE=TRUE, CHOWTEST=TRUE) #Estimate the Model myModelDefinition: #the number of behavioral equations to be estimated is 1. #The total number of coefficients is 6. # #_________________________________________ # #BEHAVIORAL EQUATION: w1 #Estimation Technique: OLS # #w1 = - 4.48873 # T-stat. -2.47402 * # # + 0.545102 (y+t-w2) # T-stat. 15.3462 *** # # + c3 TSLAG(y+t-w2,1) # PDL # # + 0.292018 time # T-stat. 5.58588 ** # #PDL: #c3 1 3 # #Distributed Lag Coefficient: c3 #Lag Coeff. Std. Error T-stat. #0 0.0413985 0.0336676 1.22963 #1 0.0493551 0.00742323 6.64873 *** #2 0.0573116 0.0265487 2.15873 #SUM 0.148065 0.0222697 # #RESTRICTIONS F-TEST: #F-value : 3.35954 #F-prob(1,5) : 0.126295 # # #STATs: #R-Squared : 0.995931 #Adjusted R-Squared : 0.993219 #Durbin-Watson Statistic : 2.43313 #Sum of squares of residuals : 0.737093 #Standard Error of Regression : 0.350498 #Log of the Likelihood Function : -0.742173 #F-statistic : 367.183 #F-probability : 2.68564e-07 #Akaike's IC : 13.4843 #Schwarz's IC : 15.8717 #Mean of Dependent Variable : 34.9909 #Number of Observations : 11 #Number of Degrees of Freedom : 6 #Current Sample (year-period) : 1925-1 / 1935-1 # # #Signif. codes: *** 0.001 ** 0.01 * 0.05 # # # #STABILITY ANALYSIS: #Behavioral equation: w1 # #Chow test: #Sample (auto) : 1936-1 / 1941-1 #F-value : 15.3457 #F-prob(6,12) : 5.34447e-05 # #Predictive Power: # #Date, Prd., Actual , Predict , Error , Std. Error , T-stat # #1936, 1 , 36.8 , 38.439 , -1.63901 , 0.547471 , -2.99378 #1937, 1 , 41 , 40.824 , 0.176033 , 0.630905 , 0.279017 #1938, 1 , 38.2 , 39.6553 , -1.4553 , 0.672192 , -2.165 #1939, 1 , 41.6 , 45.0547 , -3.45466 , 0.834433 , -4.14012 #1940, 1 , 45 , 49.0118 , -4.01179 , 0.966472 , -4.15096 #1941, 1 , 53.3 , 56.6727 , -3.37275 , 1.23486 , -2.73127 # # #...ESTIMATE OK
This function returns the frequency of a time series. In the case of a sparse xts() time series, and in other cases, the R functions xts::periodicity() and frequency() do not return BIMETS compliant values. Therefore, these functions have been extended.
## S3 method for class 'xts' frequency(x,...)## S3 method for class 'xts' frequency(x,...)
x |
Input time series. |
... |
Backward compatibility. |
This function returns the integer value stored in the attribute .bimetsFreq of the input time series, if any. Otherwise, the frequency will be calculated by using the shortest time difference between two observations, while accounting for day-saving and bissextile years.
normalizeYPNUMPERIODBIMETS indexing
#build a sparse xts() xArr<-rnorm(13) dateArr<-seq(as.Date('2000/01/01'),by='6 months',length=10) dateArr2<-seq(as.Date('2010/01/01'),by='3 months',length=3) #strange array of dates here below... dateArr3<-c(dateArr,dateArr2) dataF<-data.frame(dateArr3,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) #get bimets calculated frequency cat(frequency(xt)) #print 4... without bimets R returns 1 #...legacy periodicity() periodicity(xt)#build a sparse xts() xArr<-rnorm(13) dateArr<-seq(as.Date('2000/01/01'),by='6 months',length=10) dateArr2<-seq(as.Date('2010/01/01'),by='3 months',length=3) #strange array of dates here below... dateArr3<-c(dateArr,dateArr2) dataF<-data.frame(dateArr3,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) #get bimets calculated frequency cat(frequency(xt)) #print 4... without bimets R returns 1 #...legacy periodicity() periodicity(xt)
This function transforms a BIMETS compliant time series (as defined in is.bimets) into a time series of class ts(). The core R function as.ts() does not satisfy all the compliance control check requirements, so it has been extended. Attributes and description of the input time series will be copied to the output time series (see TIMESERIES).
fromBIMETStoTS(x = NULL, ...)fromBIMETStoTS(x = NULL, ...)
x |
Input time series that must satisfy the compliance control check defined in |
... |
Backward compatibility. |
This function returns a time series of class ts() that has the same observations of the input BIMETS time series.
fromBIMETStoXTSas.bimetsis.bimetsBIMETS indexingBIMETS configuration
#work with XTS setBIMETSconf('BIMETS_CONF_CCT','XTS') #create yearly time series xts<-TSERIES(1:10,START=c(2000,1),FREQ='A') print(is.ts(xts))#FALSE #convert to ts ts<-fromBIMETStoTS(xts) print(is.ts(ts))#TRUE print(ts) #create monthly time series xts<-TSERIES(1:10,START=c(2000,1),FREQ='M') print(is.ts(xts))#FALSE #convert to ts ts<-fromBIMETStoTS(xts) print(is.ts(ts))#TRUE print(ts) #create daily time series xts<-TSERIES(1:10,START=c(2000,1),FREQ='D') print(is.ts(xts))#FALSE #convert to ts ts<-fromBIMETStoTS(xts) print(is.ts(ts))#TRUE print(ts) #reset default setBIMETSconf('BIMETS_CONF_CCT','TS')#work with XTS setBIMETSconf('BIMETS_CONF_CCT','XTS') #create yearly time series xts<-TSERIES(1:10,START=c(2000,1),FREQ='A') print(is.ts(xts))#FALSE #convert to ts ts<-fromBIMETStoTS(xts) print(is.ts(ts))#TRUE print(ts) #create monthly time series xts<-TSERIES(1:10,START=c(2000,1),FREQ='M') print(is.ts(xts))#FALSE #convert to ts ts<-fromBIMETStoTS(xts) print(is.ts(ts))#TRUE print(ts) #create daily time series xts<-TSERIES(1:10,START=c(2000,1),FREQ='D') print(is.ts(xts))#FALSE #convert to ts ts<-fromBIMETStoTS(xts) print(is.ts(ts))#TRUE print(ts) #reset default setBIMETSconf('BIMETS_CONF_CCT','TS')
This function transforms a BIMETS compliant time series (as defined in is.bimets)
into a time series of class xts().
The core XTS function as.xts() does not satisfy all the compliance control check requirements, so it has been extended. If the output time series will have an .indexClass of type Date(), i.e. neither monthly nor quarterly, the output dates will be chosen accordingly to the BIMETS option BIMETS_CONF_DIP: if this option is set to LAST (default), the output xts() time series will have the date of the period set equal to the last day in the same period, e.g. 31 December for yearly time series, 30 June for semiannual, etc.; if the BIMETS option BIMETS_CONF_DIP is set to FIRST, the output xts() time series will have the date of the period set equal to the first day in the same period, e.g. 1 January for yearly time series, 1 July for semiannual time series on the second period, etc.
In the case of quarterly time series the .indexClass=yearqtr;
in the case of monthly time series the .indexClass=yearmon.
Attributes and description of the input time series will be copied to the output time series (see TIMESERIES)
fromBIMETStoXTS(x = NULL, ...)fromBIMETStoXTS(x = NULL, ...)
x |
Input time series that must satisfy the compliance control check defined in |
... |
Backward compatibility. |
This function returns a time series of class xts() that has the same observations of the input BIMETS time series.
fromBIMETStoTSas.bimetsis.bimetsBIMETS indexingBIMETS configuration
#create yearly time series ts<-TSERIES(1:10,START=c(2000,1),FREQ='A') print(is.xts(ts))#FALSE #convert to xts xts<-fromBIMETStoXTS(ts) print(is.xts(xts))#TRUE print(xts) #create monthly time series ts<-TSERIES(1:10,START=c(2000,1),FREQ='M') print(is.xts(ts))#FALSE #convert to xts xts<-fromBIMETStoXTS(ts) print(is.xts(xts))#TRUE print(xts) #create daily time series ts<-TSERIES(1:10,START=c(2000,1),FREQ='D') print(is.xts(ts))#FALSE #convert to xts xts<-fromBIMETStoXTS(ts) print(is.xts(xts))#TRUE print(xts) #create yearly time series with first date on period setBIMETSconf('BIMETS_CONF_DIP','FIRST') ts<-TSERIES(1:10,START=c(2000,1),FREQ='A') print(is.xts(ts))#FALSE #convert to xts xts=fromBIMETStoXTS(ts) print(is.xts(xts))#TRUE print(xts)#dates on Jan 1 #reset default setBIMETSconf('BIMETS_CONF_DIP','LAST')#create yearly time series ts<-TSERIES(1:10,START=c(2000,1),FREQ='A') print(is.xts(ts))#FALSE #convert to xts xts<-fromBIMETStoXTS(ts) print(is.xts(xts))#TRUE print(xts) #create monthly time series ts<-TSERIES(1:10,START=c(2000,1),FREQ='M') print(is.xts(ts))#FALSE #convert to xts xts<-fromBIMETStoXTS(ts) print(is.xts(xts))#TRUE print(xts) #create daily time series ts<-TSERIES(1:10,START=c(2000,1),FREQ='D') print(is.xts(ts))#FALSE #convert to xts xts<-fromBIMETStoXTS(ts) print(is.xts(xts))#TRUE print(xts) #create yearly time series with first date on period setBIMETSconf('BIMETS_CONF_DIP','FIRST') ts<-TSERIES(1:10,START=c(2000,1),FREQ='A') print(is.xts(ts))#FALSE #convert to xts xts=fromBIMETStoXTS(ts) print(is.xts(xts))#TRUE print(xts)#dates on Jan 1 #reset default setBIMETSconf('BIMETS_CONF_DIP','LAST')
This function transforms a BIMETS compliant ts time series (as defined in is.bimets) into a time series of class xts().
The core XTS function as.xts() does not satisfy all the compliance control check requirements, so it has been extended. If the output time series has an .indexClass of type Date(), i.e. neither monthly nor quarterly, the output dates are chosen accordingly to the BIMETS option BIMETS_CONF_DIP: if this option is set to LAST (default), the output xts() time series will have the date of the period set equal to the last day in the same period, e.g. 31 December for yearly time series, 30 June for semiannual, etc.; if BIMETS option BIMETS_CONF_DIP is set to FIRST, the output xts() time series will have the date of the period set equal to the first day in the same period, e.g. 1 January for yearly time series, 1 July for semiannual time series on the second period, etc.
In the case of quarterly time series the .indexClass=yearqtr;
in the case of monthly time series the .indexClass=yearmon.
Attributes and description of the input time series will be copied to the output time series (see TIMESERIES)
fromTStoXTS(x = NULL, avoidCompliance = FALSE, ...)fromTStoXTS(x = NULL, avoidCompliance = FALSE, ...)
x |
Input |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a time series of class xts() that has the same observations of the input ts time series.
fromXTStoTSas.bimetsis.bimetsBIMETS indexingBIMETS configuration
#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #BIMETS_CONF_DIP default on LAST print('yearly') t<-ts(1:20,start=c(2005,2),frequency=1) ts<-fromTStoXTS(t) print(t);print(ts) #...dates on 31 Dec print('semiannual') t<-ts(1:20,start=c(2005,2),frequency=2) ts<-fromTStoXTS(t) print(t);print(ts) #...dates on 31 Dec/30 Jun #set configuration BIMETS_CONF_DIP on FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') print('yearly') t<-ts(1:20,start=c(2005,2),frequency=1) ts<-fromTStoXTS(t) print(t);print(ts) #...dates on 1 Jan print('semiannual') t<-ts(1:20,start=c(2005,2),frequency=2) ts<-fromTStoXTS(t) print(t);print(ts) #...dates on 1 Jan/1 Jul print('quarterly') t<-ts(1:20,start=c(2004,3),frequency=4) ts<-fromTStoXTS(t) print(t);print(ts) print('monthly') t<-ts(1:20,start=c(2003,5),frequency=12) ts<-fromTStoXTS(t) print(t);print(ts) print('daily') t<-ts(1:20,start=c(2003,125),frequency=366) ts<-fromTStoXTS(t) print(t);print(ts)#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #BIMETS_CONF_DIP default on LAST print('yearly') t<-ts(1:20,start=c(2005,2),frequency=1) ts<-fromTStoXTS(t) print(t);print(ts) #...dates on 31 Dec print('semiannual') t<-ts(1:20,start=c(2005,2),frequency=2) ts<-fromTStoXTS(t) print(t);print(ts) #...dates on 31 Dec/30 Jun #set configuration BIMETS_CONF_DIP on FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') print('yearly') t<-ts(1:20,start=c(2005,2),frequency=1) ts<-fromTStoXTS(t) print(t);print(ts) #...dates on 1 Jan print('semiannual') t<-ts(1:20,start=c(2005,2),frequency=2) ts<-fromTStoXTS(t) print(t);print(ts) #...dates on 1 Jan/1 Jul print('quarterly') t<-ts(1:20,start=c(2004,3),frequency=4) ts<-fromTStoXTS(t) print(t);print(ts) print('monthly') t<-ts(1:20,start=c(2003,5),frequency=12) ts<-fromTStoXTS(t) print(t);print(ts) print('daily') t<-ts(1:20,start=c(2003,125),frequency=366) ts<-fromTStoXTS(t) print(t);print(ts)
This function transforms a BIMETS compliant xts() time series (as defined in is.bimets) into a time series of class ts(). The core R function as.ts() does not satisfy all the compliance control check requirements, so it has been extended. Attributes and description of the input time series will be copied to the output time series (see TIMESERIES).
fromXTStoTS(x = NULL, avoidCompliance = FALSE, ...)fromXTStoTS(x = NULL, avoidCompliance = FALSE, ...)
x |
Input |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a time series of class ts() that has the same observations of the input xts() time series.
fromTStoXTSas.bimetsis.bimetsBIMETS indexingBIMETS configuration
#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #set configuration BIMETS_CONF_DIP on FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') #set configuration BIMETS_CONF_CCT on XTS setBIMETSconf('BIMETS_CONF_CCT','XTS') #semiannual with Date() n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/07/01'),by='6 months',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) print(fromXTStoTS(xt)) #set configuration BIMETS_CONF_DIP on LAST setBIMETSconf('BIMETS_CONF_DIP','LAST') #yearly with Date() n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/12/31'),by='year',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) print(fromXTStoTS(xt)) #quarterly with yearqtr() n<-10 xArr<-rnorm(n+1) dateArr<-as.yearqtr('2000 Q2') + 0:n/4 dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) print(fromXTStoTS(xt)) #monthly with yearmon() n<-10 xArr<-rnorm(n+1) dateArr<-as.yearmon('Jul 2000') + 0:n/12 dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) print(fromXTStoTS(xt)) #daily with Date() n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/07/14'),by='day',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) print(fromXTStoTS(xt)) #restore defaults setBIMETSconf('BIMETS_CONF_DIP','LAST') setBIMETSconf('BIMETS_CONF_CCT','TS')#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #set configuration BIMETS_CONF_DIP on FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') #set configuration BIMETS_CONF_CCT on XTS setBIMETSconf('BIMETS_CONF_CCT','XTS') #semiannual with Date() n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/07/01'),by='6 months',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) print(fromXTStoTS(xt)) #set configuration BIMETS_CONF_DIP on LAST setBIMETSconf('BIMETS_CONF_DIP','LAST') #yearly with Date() n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/12/31'),by='year',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) print(fromXTStoTS(xt)) #quarterly with yearqtr() n<-10 xArr<-rnorm(n+1) dateArr<-as.yearqtr('2000 Q2') + 0:n/4 dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) print(fromXTStoTS(xt)) #monthly with yearmon() n<-10 xArr<-rnorm(n+1) dateArr<-as.yearmon('Jul 2000') + 0:n/12 dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) print(fromXTStoTS(xt)) #daily with Date() n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/07/14'),by='day',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) print(fromXTStoTS(xt)) #restore defaults setBIMETSconf('BIMETS_CONF_DIP','LAST') setBIMETSconf('BIMETS_CONF_CCT','TS')
This function returns the date array of selected observations, in the requested print format. Dates will be provided accordingly to the BIMETS configuration option BIMETS_CONF_DIP
(see BIMETS configuration )
GETDATE(x=NULL, index=NULL, format='%Y-%m-%d', avoidCompliance=FALSE, ...)GETDATE(x=NULL, index=NULL, format='%Y-%m-%d', avoidCompliance=FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
index |
Index of observations to be selected. The output dates will be the dates of the selected observations. If |
format |
Output print format, provided as a paste of the following codes: |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns the date array of selected observations, in the requested print format.
BIMETS configurationBIMETS indexingyq2ypym2ypdate2ypLOCSNAMELISTTSLOOKTABITELIMELS
#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #work on xts setBIMETSconf('BIMETS_CONF_CCT','XTS') #XTS yearly n<-10 xArr<-(n:1) dateArr<-seq(as.Date('2000-12-31'),by='year',length=n) dataF<-data.frame(dateArr,xArr) ts1<-xts(dataF[,2],order.by=dataF[,1]) ts1[5]<-NA print(GETDATE(ts1,5)) #...print 2004-12-31 print(GETDATE(ts1,5,'%A %d %b %Y')) #print... Friday 31 Dec 2004 print(GETDATE(ts1)) #print... "2000-12-31" "2001-12-31" ... "2009-12-31" #XTS quarterly n<-15 xArr<-(n:0) dateArr<-as.yearqtr('2000 Q1')+0:n/4 dataF<-data.frame(dateArr,xArr) ts1<-xts(dataF[,2],order.by=dataF[,1]) print(GETDATE(ts1,9,'%b %Y')) #print...Mar 2002 #XTS monthly #set configuration BIMETS_CONF_DIP to FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') n<-15 xArr<-(n:0) dateArr<-as.yearmon('Jan 2000')+0:n/12 dataF<-data.frame(dateArr,xArr) ts1<-xts(dataF[,2],order.by=dataF[,1]) print(GETDATE(ts1,9,'%b %Y')) #print...Sep 2000 #set configuration BIMETS_CONF_DIP to LAST setBIMETSconf('BIMETS_CONF_DIP','LAST') #2000 is bissextile... print(GETDATE(ts1,2)) #print... 2000-02-29 #quarter... print(GETDATE(ts1,5,'%Y Q%q')) #print... 2000 Q2 #restore default setBIMETSconf('BIMETS_CONF_CCT','TS')#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #work on xts setBIMETSconf('BIMETS_CONF_CCT','XTS') #XTS yearly n<-10 xArr<-(n:1) dateArr<-seq(as.Date('2000-12-31'),by='year',length=n) dataF<-data.frame(dateArr,xArr) ts1<-xts(dataF[,2],order.by=dataF[,1]) ts1[5]<-NA print(GETDATE(ts1,5)) #...print 2004-12-31 print(GETDATE(ts1,5,'%A %d %b %Y')) #print... Friday 31 Dec 2004 print(GETDATE(ts1)) #print... "2000-12-31" "2001-12-31" ... "2009-12-31" #XTS quarterly n<-15 xArr<-(n:0) dateArr<-as.yearqtr('2000 Q1')+0:n/4 dataF<-data.frame(dateArr,xArr) ts1<-xts(dataF[,2],order.by=dataF[,1]) print(GETDATE(ts1,9,'%b %Y')) #print...Mar 2002 #XTS monthly #set configuration BIMETS_CONF_DIP to FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') n<-15 xArr<-(n:0) dateArr<-as.yearmon('Jan 2000')+0:n/12 dataF<-data.frame(dateArr,xArr) ts1<-xts(dataF[,2],order.by=dataF[,1]) print(GETDATE(ts1,9,'%b %Y')) #print...Sep 2000 #set configuration BIMETS_CONF_DIP to LAST setBIMETSconf('BIMETS_CONF_DIP','LAST') #2000 is bissextile... print(GETDATE(ts1,2)) #print... 2000-02-29 #quarter... print(GETDATE(ts1,5,'%Y Q%q')) #print... 2000 Q2 #restore default setBIMETSconf('BIMETS_CONF_CCT','TS')
Given a time series list, this function returns intersection or union of time series' ranges.
GETRANGE( x=list(), type='INNER', avoidCompliance=FALSE, ...)GETRANGE( x=list(), type='INNER', avoidCompliance=FALSE, ...)
x |
Input list, having elements as time series of class |
type |
If |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns the common range of the input time series as a 4-integer array built by c(START_Y,START_P,END_Y,END_P). If type='INNER' and there is no intersection of time series' ranges, then this function will return a NULL.
TSJOINTSEXTENDTSMERGEMOVAVGGETYEARPERIODCUMSUM
#create ts ts1=TSERIES((1:40), START=c(2000,1), FREQ=4) ts2=TSERIES((1:40), START=c(2001,1), FREQ=4) ts3=TSERIES((1:40), START=c(2002,1), FREQ=4) myList=list(ts1,ts2,ts3) print(GETRANGE(myList)) print(GETRANGE(myList,type='OUTER'))#create ts ts1=TSERIES((1:40), START=c(2000,1), FREQ=4) ts2=TSERIES((1:40), START=c(2001,1), FREQ=4) ts3=TSERIES((1:40), START=c(2002,1), FREQ=4) myList=list(ts1,ts2,ts3) print(GETRANGE(myList)) print(GETRANGE(myList,type='OUTER'))
This function returns a two-element list (or a two-columns matrix in the case of JOIN=TRUE) built with of the years and the periods of the input time series observations. Users can provide the output list names.
GETYEARPERIOD(x=NULL, YEARS='YEAR', PERIODS='PRD', JOIN=FALSE, avoidCompliance=FALSE, ...) TSDATES(x=NULL, YEARS='YEAR', PERIODS='PRD', JOIN=FALSE, avoidCompliance=FALSE, ...)GETYEARPERIOD(x=NULL, YEARS='YEAR', PERIODS='PRD', JOIN=FALSE, avoidCompliance=FALSE, ...) TSDATES(x=NULL, YEARS='YEAR', PERIODS='PRD', JOIN=FALSE, avoidCompliance=FALSE, ...)
x |
Input time series, that must satisfy the compliance control check defined in |
YEARS |
Argument of type string that will be the output list name for the array of observation years. |
PERIODS |
Argument of type string that will be the output list name for the array of observation periods. |
JOIN |
If |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns an object of class list(). If JOIN=TRUE, this function returns a matrix.
NOELSTSERIESis.bimetsBIMETS indexingTSLEADTSINFOTSLOOKTABITELIMELS
#create quarterly ts n<-20 ts1<-TSERIES((n:1),START=c(2000,1),FREQ=4) myYP<-GETYEARPERIOD(ts1) print(myYP$YEAR) #print 2000 2000 ... print(myYP$PRD) #print 1 2 3 4 1 2 ... #create monthly ts ts1<-TSERIES((n:1),START=c(2000,1),FREQ='M') myYP<-GETYEARPERIOD(ts1) print(myYP$YEAR) #print 2000 2000 ... print(myYP$PRD) #print 1 2 3 4 5 6 7 ... #create yearly ts ts1<-TSERIES((1:n),START=c(2000,1),FREQ=1) myYP<-GETYEARPERIOD(ts1,YEARS='YEARSS', PERIODS='PRDSS') print(myYP$YEARSS) #print 2000 2001 2002 ... print(myYP$PRDSS) #print 1 1 1 1..... #JOIN=TRUE ts1<-TSERIES((n:1),START=c(2000,1),FREQ='M') myYP<-GETYEARPERIOD(ts1,JOIN=TRUE) print(myYP) #print 2000 2000 ... # [,1] [,2] #[1,] 2000 1 #[2,] 2000 2 #[3,] 2000 3 #...#create quarterly ts n<-20 ts1<-TSERIES((n:1),START=c(2000,1),FREQ=4) myYP<-GETYEARPERIOD(ts1) print(myYP$YEAR) #print 2000 2000 ... print(myYP$PRD) #print 1 2 3 4 1 2 ... #create monthly ts ts1<-TSERIES((n:1),START=c(2000,1),FREQ='M') myYP<-GETYEARPERIOD(ts1) print(myYP$YEAR) #print 2000 2000 ... print(myYP$PRD) #print 1 2 3 4 5 6 7 ... #create yearly ts ts1<-TSERIES((1:n),START=c(2000,1),FREQ=1) myYP<-GETYEARPERIOD(ts1,YEARS='YEARSS', PERIODS='PRDSS') print(myYP$YEARSS) #print 2000 2001 2002 ... print(myYP$PRDSS) #print 1 1 1 1..... #JOIN=TRUE ts1<-TSERIES((n:1),START=c(2000,1),FREQ='M') myYP<-GETYEARPERIOD(ts1,JOIN=TRUE) print(myYP) #print 2000 2000 ... # [,1] [,2] #[1,] 2000 1 #[2,] 2000 2 #[3,] 2000 3 #...
Bimets package extends the way users can access and modify time series data.
SELECTING BY YEAR-PERIOD: Users can select observations by providing the related year and period . Selection and modification of data require the double square bracket syntax,
e.g. ts[[year,period]] <- value, given year and period as positive integers.
Users can also assign an array of values to the input time series, starting from the [[year,period]] provided,
i.e. ts[[year,period]] <- c(value1,value2,...,valueN): in this case the input time series will be eventually extended in order to sequentially insert all values of the provided array c(value1,value2,...,valueN) starting from the provided [[year,period]] (see example).
Users can select observations also by using a single bi-dimensional argument, e.g. ts[[start]], and by using two bi-dimensional arguments ts[[start,end]], given start <- c(year1,period1); end <- c(year2,period2): in this case all observation in TSRANGE=c(year1,period1,year2,period2) will be returned.
Assignments by using two-dimensional arguments are also allowed, e.g. ts[[start]] <- value; ts[[start,end]] <- value; ts[[start,end]] <- c(value1,...,valueN) (see example)
SELECTING BY DATE: users can select a single observation by date by using the syntax ts['Date'] and multiple observations by using ts['StartDate/EndDate'] or ts['StartDate'+(0:n)/f], given f as frequency, and n as observations count.
Data modification follows the same syntax: ts['Date'] <- value, ts['Date/Date'] <- c(value1,value2,...,valueN), etc. Users can also provide the string representing only the year of selection, or the year and the month of selection. For quarterly and monthly time series it is possible to select dates by using instances of class yearmon() and yearqtr() (See example).
SELECTING BY INDICES: (core R) Users can select observations by simply providing the array of requested indices,
e.g. ts[c(idx1,idx2,...,idxN)] while reading and ts[c(idx1,idx2,...,idxN)] <- c(value1,value2,...,valueN) while modifying time series data.
GETDATEBIMETS configurationdate2ypyq2ypym2ypas.bimetsis.bimetsLOCSNAMELISTTABITELIMELS
#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #monthly #------------------------------- print('MONTHLY GET by DATE') n <- 25 #create ts ts1 <- TIMESERIES((0:n),START=c(2000,1),FREQ=12) print(ts1['2001-01']) #get Jan 2001 print(ts1[as.yearmon('Jan 2001')]) #get Jan 2001 print(ts1['2000-09/2001-01']) #get data from Sep 2000 to Jan 2001 print(ts1['2000-09/']) #get data from Sep 2000 print(ts1['/2001-01']) #get data till Jan 2001 print(ts1['2001']) #gat all data in year 2001 #get 3 consecutive months starting from Jan 2001 print(ts1[as.yearmon('Jan 2001')+ 0:2/12]) print(ts1[c(2,4,5)]) #get observation number 2,4 and 5 print('MONTHLY GET by YEAR-PERIOD') print(ts1[[2000,5]]) #get year 2000 period 5 #get year 2010 period 1 (out of range) tryCatch({print(ts1[[2010,1]])},error=function(e){cat(e$message)}) print(ts1[[2002,2]]) #get year 2002 period 2 start <- c(2001,2) end <- c(2001,4) print(ts1[[start]]) #get year 2001 period 2 print(ts1[[start,end]]) #get from year-period 2001-2 to 2001-4 print('MONTHLY SET by DATE') ts1['2000-08'] <- 9.9 #assign to Aug 2000 ts1[as.yearmon('Feb 2001')] <- 8.8 #assign to Feb 2001 #assign 8.8 on Feb 2001 and give warning ts1[as.yearmon('Feb 2001')]=c(8.8,7.7) #assign same value to all observation in range Sep 2000 - Jan 2001 ts1['2000-09/2001-01'] <- 11.11 #assign repeatedly the two values to each observation starting from Sep 2001 ts1['2001-09/'] <- c(1.1,2.2) print(ts1) print('MONTHLY SET by YEAR-PERIOD') ts1[[2000,5]] <- NA #set year 2000 period 5 #assign an array starting from year 2002 period 2 (extend time series) ts1[[2002,2]] <- c(-1,-2,-3,-4,-5) TABIT(ts1) #set by bi-dimensional arrays ts1 <- TIMESERIES((0:n),START=c(2000,1),FREQ=12) ts1[[c(2000,12)]] <- NA start <- c(2001,2) end <- c(2001,4) ts1[[start,end]] <- 0 #assign single value TABIT(ts1) ts1[[start,end]] <- c(-2,-4,-6) #assign multiple values TABIT(ts1) #quarterly #------------------------------- print('QUARTERLY GET by DATE') #create ts ts1 <- TSERIES((0:n),START=c(2000,1),FREQ=4) print(ts1[as.yearqtr('2001 Q1')]) #get 2001 Q1 print(ts1['2001']) #get all data in year 2001 #get 4 consecutive quarters starting from 2002 Q2 print(ts1[as.yearqtr('2002 Q2')+ 0:3/4]) print(ts1['2003/']) #gat all data from 2003 Q1 print('QUARTERLY GET by YEAR-PERIOD') print(ts1[[2002,4]]) #get year 2002 period 4 start <- c(2001,2) end <- c(2001,4) print(ts1[[start]]) #get year 2001 period 2 print(ts1[[start,end]]) #get from year-period 2001-2 to 2001-4 print('QUARTERLY SET by DATE') ts1[as.yearqtr('2001 Q1')] <- 7.7 #assign to 2001 Q1 ts1['2002'] <- NA #assign to all observations of 2002 #assign to 3 quaters starting from 2003 Q2 ts1[as.yearqtr('2003 Q2')+ 0:2/4] <- 0 ts1['2004/'] <- -1 #assign to all observations starting from 2004 TABIT(ts1) print('QUARTERLY SET by YEAR-PERIOD') ts1[[2005,4]] <- c(1,2,3) #assign array starting from year 2005 period 4 TABIT(ts1) #set by bi-dimensional arrays ts1 <- TIMESERIES((0:n),START=c(2000,1),FREQ=4) ts1[[c(2000,12)]] <- NA start <- c(2001,2) end <- c(2001,4) ts1[[start,end]] <- 0 #assign single value TABIT(ts1) ts1[[start,end]] <- c(-2,-4,-6) #assign multiple values TABIT(ts1) #yearly #------------------------------- print('YEARLY GET by DATE') #create ts ts1 <- TSERIES((1:n),START=c(2000,1),FREQ=1) print(ts1['2002-12-31']) #get 2002 data print(ts1['2002']) #get 2002 data print(ts1['2000/2004']) #get data from 2000 to 2004 print(ts1['2005/']) #get data starting from 2005 print('YEARLY GET by YEAR-PERIOD') print(ts1[[2005,1]]) #get year 2005 #get year 2032 (out of range) tryCatch({print(ts1[[2032,1]])},error=function(e){cat(e$message)}) start <- c(2001,1) end <- c(2002,1) print(ts1[[start]]) #get year 2001 print(ts1[[start,end]]) #get from year 2001 to 2002 print('YEARLY SET by DATE') ts1['2004'] <- NA #assign to 2004 ts1['2007/'] <- 0.0 #assign starting from 2007 ts1['2000/2002'] <- -1 #assign in range 2000/2002 TABIT(ts1) print('YEARLY SET by YEAR-PERIOD') ts1[[2005,1]] <- NA #assign to 2005 ts1[[2014,1]] <- c(-1,-2,-3) #assign array starting from 2014 (extend series) TABIT(ts1) #set by bi-dimensional arrays ts1 <- TIMESERIES((0:n),START=c(2000,1),FREQ=1) ts1[[c(2000,12)]] <- NA start <- c(2001,1) end <- c(2002,1) ts1[[start,end]] <- 0 #assign single value TABIT(ts1) ts1[[start,end]] <- c(-2,-4) #assign multiple values TABIT(ts1) #daily #------------------------------- print('DAILY GET by DATE') #create ts ts1 <- TSERIES((1:n),START=c(2000,1),FREQ='D') print(ts1['2000-01-12']) #get Jan 12, 2000 data print('DAILY GET by YEAR-PERIOD') print(ts1[[2000,14]]) #get year 2000 period 14 #get year 2032 (out of range) tryCatch({print(ts1[[2032,1]])},error=function(e){cat(e$message)}) print('DAILY SET by DATE') ts1['2000-01-15'] <- NA #assign to Jan 15, 2000 TABIT(ts1) print('DAILY SET by YEAR-PERIOD') ts1[[2000,3]] <- NA #assign to Jan 3, 2000 #assign array starting from 2000 period 35 (extend series) ts1[[2000,35]] <- c(-1,-2,-3) TABIT(ts1)#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #monthly #------------------------------- print('MONTHLY GET by DATE') n <- 25 #create ts ts1 <- TIMESERIES((0:n),START=c(2000,1),FREQ=12) print(ts1['2001-01']) #get Jan 2001 print(ts1[as.yearmon('Jan 2001')]) #get Jan 2001 print(ts1['2000-09/2001-01']) #get data from Sep 2000 to Jan 2001 print(ts1['2000-09/']) #get data from Sep 2000 print(ts1['/2001-01']) #get data till Jan 2001 print(ts1['2001']) #gat all data in year 2001 #get 3 consecutive months starting from Jan 2001 print(ts1[as.yearmon('Jan 2001')+ 0:2/12]) print(ts1[c(2,4,5)]) #get observation number 2,4 and 5 print('MONTHLY GET by YEAR-PERIOD') print(ts1[[2000,5]]) #get year 2000 period 5 #get year 2010 period 1 (out of range) tryCatch({print(ts1[[2010,1]])},error=function(e){cat(e$message)}) print(ts1[[2002,2]]) #get year 2002 period 2 start <- c(2001,2) end <- c(2001,4) print(ts1[[start]]) #get year 2001 period 2 print(ts1[[start,end]]) #get from year-period 2001-2 to 2001-4 print('MONTHLY SET by DATE') ts1['2000-08'] <- 9.9 #assign to Aug 2000 ts1[as.yearmon('Feb 2001')] <- 8.8 #assign to Feb 2001 #assign 8.8 on Feb 2001 and give warning ts1[as.yearmon('Feb 2001')]=c(8.8,7.7) #assign same value to all observation in range Sep 2000 - Jan 2001 ts1['2000-09/2001-01'] <- 11.11 #assign repeatedly the two values to each observation starting from Sep 2001 ts1['2001-09/'] <- c(1.1,2.2) print(ts1) print('MONTHLY SET by YEAR-PERIOD') ts1[[2000,5]] <- NA #set year 2000 period 5 #assign an array starting from year 2002 period 2 (extend time series) ts1[[2002,2]] <- c(-1,-2,-3,-4,-5) TABIT(ts1) #set by bi-dimensional arrays ts1 <- TIMESERIES((0:n),START=c(2000,1),FREQ=12) ts1[[c(2000,12)]] <- NA start <- c(2001,2) end <- c(2001,4) ts1[[start,end]] <- 0 #assign single value TABIT(ts1) ts1[[start,end]] <- c(-2,-4,-6) #assign multiple values TABIT(ts1) #quarterly #------------------------------- print('QUARTERLY GET by DATE') #create ts ts1 <- TSERIES((0:n),START=c(2000,1),FREQ=4) print(ts1[as.yearqtr('2001 Q1')]) #get 2001 Q1 print(ts1['2001']) #get all data in year 2001 #get 4 consecutive quarters starting from 2002 Q2 print(ts1[as.yearqtr('2002 Q2')+ 0:3/4]) print(ts1['2003/']) #gat all data from 2003 Q1 print('QUARTERLY GET by YEAR-PERIOD') print(ts1[[2002,4]]) #get year 2002 period 4 start <- c(2001,2) end <- c(2001,4) print(ts1[[start]]) #get year 2001 period 2 print(ts1[[start,end]]) #get from year-period 2001-2 to 2001-4 print('QUARTERLY SET by DATE') ts1[as.yearqtr('2001 Q1')] <- 7.7 #assign to 2001 Q1 ts1['2002'] <- NA #assign to all observations of 2002 #assign to 3 quaters starting from 2003 Q2 ts1[as.yearqtr('2003 Q2')+ 0:2/4] <- 0 ts1['2004/'] <- -1 #assign to all observations starting from 2004 TABIT(ts1) print('QUARTERLY SET by YEAR-PERIOD') ts1[[2005,4]] <- c(1,2,3) #assign array starting from year 2005 period 4 TABIT(ts1) #set by bi-dimensional arrays ts1 <- TIMESERIES((0:n),START=c(2000,1),FREQ=4) ts1[[c(2000,12)]] <- NA start <- c(2001,2) end <- c(2001,4) ts1[[start,end]] <- 0 #assign single value TABIT(ts1) ts1[[start,end]] <- c(-2,-4,-6) #assign multiple values TABIT(ts1) #yearly #------------------------------- print('YEARLY GET by DATE') #create ts ts1 <- TSERIES((1:n),START=c(2000,1),FREQ=1) print(ts1['2002-12-31']) #get 2002 data print(ts1['2002']) #get 2002 data print(ts1['2000/2004']) #get data from 2000 to 2004 print(ts1['2005/']) #get data starting from 2005 print('YEARLY GET by YEAR-PERIOD') print(ts1[[2005,1]]) #get year 2005 #get year 2032 (out of range) tryCatch({print(ts1[[2032,1]])},error=function(e){cat(e$message)}) start <- c(2001,1) end <- c(2002,1) print(ts1[[start]]) #get year 2001 print(ts1[[start,end]]) #get from year 2001 to 2002 print('YEARLY SET by DATE') ts1['2004'] <- NA #assign to 2004 ts1['2007/'] <- 0.0 #assign starting from 2007 ts1['2000/2002'] <- -1 #assign in range 2000/2002 TABIT(ts1) print('YEARLY SET by YEAR-PERIOD') ts1[[2005,1]] <- NA #assign to 2005 ts1[[2014,1]] <- c(-1,-2,-3) #assign array starting from 2014 (extend series) TABIT(ts1) #set by bi-dimensional arrays ts1 <- TIMESERIES((0:n),START=c(2000,1),FREQ=1) ts1[[c(2000,12)]] <- NA start <- c(2001,1) end <- c(2002,1) ts1[[start,end]] <- 0 #assign single value TABIT(ts1) ts1[[start,end]] <- c(-2,-4) #assign multiple values TABIT(ts1) #daily #------------------------------- print('DAILY GET by DATE') #create ts ts1 <- TSERIES((1:n),START=c(2000,1),FREQ='D') print(ts1['2000-01-12']) #get Jan 12, 2000 data print('DAILY GET by YEAR-PERIOD') print(ts1[[2000,14]]) #get year 2000 period 14 #get year 2032 (out of range) tryCatch({print(ts1[[2032,1]])},error=function(e){cat(e$message)}) print('DAILY SET by DATE') ts1['2000-01-15'] <- NA #assign to Jan 15, 2000 TABIT(ts1) print('DAILY SET by YEAR-PERIOD') ts1[[2000,3]] <- NA #assign to Jan 3, 2000 #assign array starting from 2000 period 35 (extend series) ts1[[2000,35]] <- c(-1,-2,-3) TABIT(ts1)
This function rebases an input time series to the value of 100 in the year selected by the BASEYEAR argument. If the input time series frequency is greater than one, the initial reference is set to the average value of the input time series observations that lie in the BASEYEAR.
INDEXNUM(x=NULL, BASEYEAR=NULL, avoidCompliance=FALSE, ...)INDEXNUM(x=NULL, BASEYEAR=NULL, avoidCompliance=FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
BASEYEAR |
Rebasing year. |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a BIMETS time series.
TSJOINTSEXTENDTSMERGEMOVAVGGETYEARPERIODCUMSUM
#create yearly ts n<-20 ts1<-TSERIES(1:n,START=c(2000,1),FREQ=1) TABIT(ts1, INDEXNUM(ts1,2005)) #quarterly ts1<-TSERIES(1:n,START=c(2000,1),FREQ=4) ts1[5]<-NA TABIT(ts1, INDEXNUM(ts1,2000))#create yearly ts n<-20 ts1<-TSERIES(1:n,START=c(2000,1),FREQ=1) TABIT(ts1, INDEXNUM(ts1,2005)) #quarterly ts1<-TSERIES(1:n,START=c(2000,1),FREQ=4) ts1[5]<-NA TABIT(ts1, INDEXNUM(ts1,2000))
A command such INTS(i,j) returns a one-dimensional array built of the integers i, i+1, i+2, ..., j when i, j are both scalars, and j is greater than i. When j is less than i, the command shown above defines a one-dimensional array built of the integers i, i-1, i-2, ..., j.
Users can specify the k increment using a syntax like INTS(i, j, k) which defines a one-dimensional array built of the values i, i+k, i+2*k, ..., i+N*k.
The value of the last element of the array is the maximum value of i+N*k that is less than or equal to j, for positive k. For negative k, the value of the last element of the array is the minimum value of i+N*k that is greater than or equal to j.
The command can be used with one parameter by using a syntax like INTS(i) where i is a positive scalar. The result is a one-dimensional array built with the integers 1, 2, 3, ..., i. When i is less than 1, the array is built with the integers -1, -2, ..., -i.
INTS(FROM=NULL, TO=NULL, BY=NULL, ...)INTS(FROM=NULL, TO=NULL, BY=NULL, ...)
FROM |
The first integer of the sequence. If arguments |
TO |
The last integer of the sequence. |
BY |
The increment between two elements of the sequence. |
... |
Backward compatibility. |
This function returns an object of class c().
TSJOINTSEXTENDTSMERGEMOVAVGGETYEARPERIODTSLAGTSINFOTABITELIMELS
print(INTS(10,1,-2)) #... 10 8 6 4 2 #...Error in INTS(10, 1, -0.5) : INTS(): inputs must be integers. tryCatch({print(INTS(10,1,-0.5));},error=function(e){cat(e$message)}) print(INTS(10)) #... 1 2 3 4 5 6 7 8 9 10 print(INTS(-10)) # -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 # Error in INTS(0) : INTS(): magnitude must be >=1 tryCatch({print(INTS(0));},error=function(e){cat(e$message)}) print(INTS(-10,-45)) # -10 -11 -12 ... -41 -42 -43 -44 -45 #...Error in seq.default(FROM, TO, BY) : wrong sign in 'by' argument tryCatch({print(INTS(-10,-45,3));},error=function(e){cat(e$message)}) print(INTS(-10,-45,-3)) # -10 -13 -16 -19 -22 -25 -28 -31 -34 -37 -40 -43print(INTS(10,1,-2)) #... 10 8 6 4 2 #...Error in INTS(10, 1, -0.5) : INTS(): inputs must be integers. tryCatch({print(INTS(10,1,-0.5));},error=function(e){cat(e$message)}) print(INTS(10)) #... 1 2 3 4 5 6 7 8 9 10 print(INTS(-10)) # -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 # Error in INTS(0) : INTS(): magnitude must be >=1 tryCatch({print(INTS(0));},error=function(e){cat(e$message)}) print(INTS(-10,-45)) # -10 -11 -12 ... -41 -42 -43 -44 -45 #...Error in seq.default(FROM, TO, BY) : wrong sign in 'by' argument tryCatch({print(INTS(-10,-45,3));},error=function(e){cat(e$message)}) print(INTS(-10,-45,-3)) # -10 -13 -16 -19 -22 -25 -28 -31 -34 -37 -40 -43
This function checks the compliance of the input time series that must verify the following BIMETS requirements:
- the input time series must be of the class defined in BIMETS_CONF_CCT (see BIMETS configuration)
- If BIMETS_CONF_CCT='TS' the input time series must be of class ts, univariate, with at least one observation and with a frequency f=1, 2, 3, 4, 12, 24, 36, 53 or 366 per year.
- if BIMETS_CONF_CCT='XTS' the input time series must be of class xts, univariate, with at least one observation and with a frequency f=1, 2, 3, 4, 12, 24, 36, 53 or 366 per year; the input time series must also be stricty regular, i.e. without any temporal discontinuity, and must have an .indexClass of type yearmon() for monthly time series, of type yearqtr() for quarterly time series and of type Date() for any other frequency. If configuration option BIMETS_CONF_DIP='LAST', i.e. the default value, the provided observation dates of the input xts() time series must be the last dates in the period, e.g. Dec. 31 for yearly time series, Jun. 30 for the first period in a semiannual time series, etc.; If configuration option BIMETS_CONF_DIP='FIRST' the provided observation dates of the input xts() time series must be the first dates in the period, e.g. Jan. 1 for an yearly time series, Jul. 1 for the second period in a semiannual time series, etc.;
BIMETS package functions return time series that are compliant to the above requirements.
The compliance check can be locally disabled by using the function argument avoidCompliance=TRUE, that is available in almost all package functions. The compliance check of a BIMETS generated time series can be avoided; moreover, disabling the control check can speed up the execution time, and is suggested when users concatenate several call to the package functions, e.g. the compliance check of the ts2 time series in the following example can be avoided: ts2=TSLAG(ts1);ts3=TSDELTA(ts2,avoidCompliance=TRUE);.
Time series must lie in the year range 1800-2199: in this range the conversion between a date and the related year-period (and vice versa) has been hardcoded in order to speed up the code execution.
If the compliance check is disabled, i.e. avoidCompliance=TRUE and the input time series does not verify all the above requirements, the package functions can have an erroneous behavior. Should any doubt arise, we suggest to call the package functions using the default arguments; we also suggest to create time series object by using the command TIMESERIES.
is.bimets(x = NULL, suppressErrors=TRUE, ...)is.bimets(x = NULL, suppressErrors=TRUE, ...)
x |
Input time series. |
suppressErrors |
If |
... |
Backward compatibility. |
This function returns a logical value TRUE/FALSE whenever the input time series is compliant to the above BIMETS requirements. If the test fails and suppressErrors=FALSE this function will throw an error.
as.bimetsTIMESERIESBIMETS indexingBIMETS configurationfromBIMETStoTSfromBIMETStoXTS
#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #set day in period to last setBIMETSconf('BIMETS_CONF_DIP','LAST') #set constructor class type setBIMETSconf('BIMETS_CONF_CCT','XTS') #create an xts xt<-TIMESERIES(1:10,START=c(2000,1),FREQ='A') print(xt); #...dates are at Dec 31 print(is.bimets(xt)) #...TRUE #change setting setBIMETSconf('BIMETS_CONF_DIP','FIRST') print(is.bimets(xt)) #...FALSE #set constructor class type setBIMETSconf('BIMETS_CONF_CCT','TS') #bivariate ts tsBiv<-ts(matrix(c(1,2,3,4,5,6),nrow=3,ncol=2),start=c(2000,1),frequency=1) print(is.bimets(tsBiv)) #...FALSE #...error tryCatch({is.bimets(tsBiv,suppressError=FALSE)}, error=function(e){cat(e$message)});try({is.bimets(tsBiv,suppressError=FALSE)}) #ts year n<-10 xArr<-rnorm(n) t<-ts(data=xArr,start=c(2000,1),frequency=1) cat('is compliant?',is.bimets(t),'\n') #ts semestral n<-10 xArr<-rnorm(n) t<-ts(data=xArr,start=c(2000,1),frequency=2) cat('is compliant?',is.bimets(t),'\n') #set configuration BIMETS_CONF_DIP on FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') #work with XTS setBIMETSconf('BIMETS_CONF_CCT','XTS') #xts yearly with dates n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/01/01'),by='year',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) cat('is compliant?',is.bimets(xt),'\n') #xts daily n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/01/01'),by='day',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) cat('is compliant?',is.bimets(xt),'\n') #xts monthly with dates n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/01/01'),by='month',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) cat('monthly with dates is compliant? ',is.bimets(xt),'\n') #...false #xts monthly with yearmon n<-10 xArr<-rnorm(n+1) dateArr<-as.yearmon('Jan 2001')+0:n/12 dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) cat('monthly with yearmon is compliant? ',is.bimets(xt),'\n') #...true #restore defaults setBIMETSconf('BIMETS_CONF_CCT','TS') setBIMETSconf('BIMETS_CONF_DIP','LAST')#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #set day in period to last setBIMETSconf('BIMETS_CONF_DIP','LAST') #set constructor class type setBIMETSconf('BIMETS_CONF_CCT','XTS') #create an xts xt<-TIMESERIES(1:10,START=c(2000,1),FREQ='A') print(xt); #...dates are at Dec 31 print(is.bimets(xt)) #...TRUE #change setting setBIMETSconf('BIMETS_CONF_DIP','FIRST') print(is.bimets(xt)) #...FALSE #set constructor class type setBIMETSconf('BIMETS_CONF_CCT','TS') #bivariate ts tsBiv<-ts(matrix(c(1,2,3,4,5,6),nrow=3,ncol=2),start=c(2000,1),frequency=1) print(is.bimets(tsBiv)) #...FALSE #...error tryCatch({is.bimets(tsBiv,suppressError=FALSE)}, error=function(e){cat(e$message)});try({is.bimets(tsBiv,suppressError=FALSE)}) #ts year n<-10 xArr<-rnorm(n) t<-ts(data=xArr,start=c(2000,1),frequency=1) cat('is compliant?',is.bimets(t),'\n') #ts semestral n<-10 xArr<-rnorm(n) t<-ts(data=xArr,start=c(2000,1),frequency=2) cat('is compliant?',is.bimets(t),'\n') #set configuration BIMETS_CONF_DIP on FIRST setBIMETSconf('BIMETS_CONF_DIP','FIRST') #work with XTS setBIMETSconf('BIMETS_CONF_CCT','XTS') #xts yearly with dates n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/01/01'),by='year',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) cat('is compliant?',is.bimets(xt),'\n') #xts daily n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/01/01'),by='day',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) cat('is compliant?',is.bimets(xt),'\n') #xts monthly with dates n<-10 xArr<-rnorm(n) dateArr<-seq(as.Date('2000/01/01'),by='month',length=n) dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) cat('monthly with dates is compliant? ',is.bimets(xt),'\n') #...false #xts monthly with yearmon n<-10 xArr<-rnorm(n+1) dateArr<-as.yearmon('Jan 2001')+0:n/12 dataF<-data.frame(dateArr,xArr) xt<-xts(dataF[,2],order.by=dataF[,1]) cat('monthly with yearmon is compliant? ',is.bimets(xt),'\n') #...true #restore defaults setBIMETSconf('BIMETS_CONF_CCT','TS') setBIMETSconf('BIMETS_CONF_DIP','LAST')
This function parses a MDL model definition and creates an equivalent R data structure that can be estimated and simulated. The input model definition can be either an external plain text file or a character variable.
LOAD_MODEL( modelFile=NULL, modelText=NULL, quietly=FALSE, oldStyleModel=FALSE, ...)LOAD_MODEL( modelFile=NULL, modelText=NULL, quietly=FALSE, oldStyleModel=FALSE, ...)
modelFile |
The path to the text file containing the |
modelText |
The |
quietly |
If |
oldStyleModel |
Backward compatibility. |
... |
Backward compatibility. |
This function returns a BIMETS model object containing all the information gathered the input model definition's parsing.
A BIMETS model created with the LOAD_MODEL function can be viewed as a complex R list() containing the following elements (see example):
- rawData and cleanModel: string arrays containing the original model definition. cleanModel is a clean version of the model definition, i.e. without comments, blank lines, etc.;
- behaviorals and identities: sub-lists containing all the information gathered from the behavioral and the identity definitions. This sub lists are described later in this page;
- vendog and vexog: string array containing the names of the endogenous and exogenous variables of the model; the former is also subsetted into vendogBehaviorals and vendogIdentities
- totNumEqs, totNumIds and eqCoeffNum: integer variables containing the behaviorals count, the identities count and the coefficients count of the model;
- max_lag: the max lag of the model, i.e. the highest number of periods a time series of the model is lagged by in the MDL definition. It also accounts for recursive lagging
(e.g. TSLAG(...TSLAG(...)...)), PDLs and for the order of the error autocorrelation, if any;
- max_lead: the max lead of the model, i.e. the highest number of periods a time series of the model is leaded by in the MDL definition. It also accounts for recursive leading
(e.g. TSLEAD(...TSLEAD(...)...));
- modelName: the name of the model, copied from the input file name or from the input character variable name containing the model definition;
- bimets_version: the version of the BIMETS package the current model has been built with.
- incidence_matrix: the incidence matrix built from the model equations; it is a square matrix in which each row and each column represent an endogenous variable. If the (i,j) element is equal to 1 then in the model definition the current value of the endogenous variable referred by the i-row directly depends on the current value of the endogenous variable referred by the j-column. (see example)
- vpre, vblocks: the simulation process takes advantage of an appropriate ordering of the equations to increase the performances by iteratively solving only one subset of equations, while the other equations are solved straightforwardly. More details in "The Optimal Reordering" section in SIMULATE help pages (Ref: Don Gallo - Solving large sparse systems of equations in econometric models - Journal of Forecasting 1987 and Numerical methods for simulation and optimal control of large-scale macroeconomic models - Nepomiastchy, Rachidi, Ravelli - 1980). The optimal reordering of the model equations is achieved by using an iterative algorithm applied to the incidence matrix, that produces 1+3*N ordered arrays of endogenous variables, given N the length of the vblocks list:
1. vpre is the ordered list containing the names of the endogenous pre-recursive variables to be sequentially computed (once per simulation period) before the simulation iterative algorithm takes place;
2. vblocks[[i]]$vsim, i=1..N (the simultaneous subset) is the ordered list containing the names of the endogenous variables to be sequentially computed during each iteration of the simulation iterative algorithm in the current block i;
3. vblocks[[i]]$vfeed, i=1..N is the list containing the names of the endogenous feedback variables in the current block i; generally vfeed are the last variables in the ordered vsim list;
4. vblocks[[i]]$vpost, i=1..N is the ordered list containing the names of the endogenous post-recursive variables to be sequentially computed (once per simulation period) after the simulation iterative algorithm has found a solution in the simultaneous subset in the current block i;
In forward-looking models, the incidence matrix and the equations reordering depend on the simulation periods count, therefore the attributes incidence_matrix, vpre and vblocks will be available only after a simulation has been completed, and will be available to users in the model$simulation[['__SIM_PARAMETERS__']] lists.
BEHAVIORALS and IDENTITIES
The elements 'behaviorals' and 'identities' of the BIMETS model are named lists that contain information on behaviorals and identities of the model. In both of this two lists, the name of each element is the name of the behavioral or the identity the data refer to, as specified in the model definition file: e.g. given a BIMETS model named myModel, the information on a behavioral named cn (i.e there exists a "BEHAVIORAL> cn" in the MDL definition of the model) is stored into myModel$behaviorals$cn.
Behavioral elements have the following components:
- eq: the equation of the behavioral, as a character variable;
- eqCoefficientsNames: the names of the coefficients (the original ones and eventually the ones created by the PDL> expansion);
- eqCoefficientsNamesOriginal: the names of the original coefficients;
- eqComponentsNames: the names of endogenous and exogenous variables that appear in the behavioral equation;
- eqComponentsNamesBehaviorals: the names of behavioral endogenous variables that appear in the behavioral equation;
- eqComponentsNamesIdentities: the names of identity endogenous variables that appear in the behavioral equation;
- eqComponentsNamesExogenous: the names of exogenous variables that appear in the behavioral equation;
- tsrange: the estimation time range as a 4 integer array;
- eqRegressorsNames: a character array containing the regressor expressions (the original ones and eventually the ones created by the PDL> expansion);
- eqRegressorsNamesOriginal: a character array containing the expressions of the original regressors;
- errorRaw: the original definition of the error autocorrelation, if any (see MDL);
- errorType: the type of the error structure;
- errorDim: the dimension of the error autocorrelation;
- eqSimExp: the R optimized expression of the current behavioral equation; it is used in the simulation algorithm and is derived by parsing the eqSimExpText text element;
- eqSimExpLeadedText: it is derived by transforming the leaded time series that apper in the current behavioral equation, if any, and it is used, during the simulation of forward-looking models, to build up the leadsEqSimExpText and leadsEqSimExp elements, that contain, per each period in the simulation TSRANGE, the leaded and accordingly transformed equation (see "Rational Expectation Models" section in SIMULATE help page));
- matrixR: the R Lagrange matrix that is used in restriction analysis (see MDL);
- vectorR: the r Lagrange vector that is used in restriction analysis (see MDL);
- restrictRaw: the original definition of the coefficient restrictions, if any.
- pdlRaw: the original definition of the PDL restrictions, if any (see example and MDL).
- pdlRestrictionMatrix: the R Lagrange matrix that is used in PDL restriction analysis (see example and MDL);
- IVComponentsNames: the names of endogenous and exogenous variables that appear in the instrumental variables equations, if any;
- iv: the original definitions of instrumental variables, if any.
- lhsFun: the LHS function that appers in the current behavioral equations;
For example, given a BIMETS model named myModel, the information on a technical identity named y (i.e there exists an "IDENTITY> y" in the MDL definition of the model) is stored in myModel$identities$y.
Identity elements have the following components:
- eqRaw: the original equations of the identity (more than one if the identity has multiple equations and has IF> conditions), as a character variable (see example and MDL);
- ifRaw, ifCondition: the original and the optimized IF> conditions, if any, of the identity, as a character variable;
- eqFull: the full expression of the identity, composed with IF> conditions and related equations (see example), as a character variable;
- eqComponentsNames: the names of endogenous and exogenous variables that appear in the identity equation;
- eqComponentsNamesBehaviorals: the names of behavioral endogenous variables that appear in the identity equation;
- eqComponentsNamesIdentities: the names of identity endogenous variables that appear in the identity equation;
- eqSimExp: the R optimized expression of the current identity equation; it is used in the simulation algorithm and is derived by parsing the eqSimExpText text element;
- eqSimExpLeadedText: it is derived by transforming the leaded time series that apper in the current identity equation, if any, and it is used, during the simulation of forward-looking models, to build up the leadsEqSimExpText and leadsEqSimExp elements, that contain, per each period in the simulation TSRANGE, the leaded and accordingly transformed equation (see "Rational Expectation Models" section in SIMULATE help page));
- hasIF: boolean, TRUE if the identity has an IF> condition;
- multipleLhsFun: the list of the LHS functions that apper in the equations related to the current identity;
MDLLOAD_MODEL_DATAESTIMATESIMULATESTOCHSIMULATEMULTMATRIXRENORMTIMESERIESBIMETS indexingBIMETS configuration
#define model myModelDefinition<- "MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment BEHAVIORAL> i TSRANGE 1923 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END" #load model myModel<-LOAD_MODEL(modelText=myModelDefinition) #retrieve model structure... #get definition myModel$cleanModel # [1] "BEHAVIORAL> cn" # [2] "TSRANGE 1925 1 1941 1" # [3] "EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2)" # [4] "COEFF> a1 a2 a3 a4" # [5] "ERROR> AUTO(2)" # [6] "BEHAVIORAL> i" # [7] "TSRANGE 1923 1 1941 1" # [8] "EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1)" # [9] "COEFF> b1 b2 b3 b4" #[10] "RESTRICT> b2 + b3 = 1" #[11] "BEHAVIORAL> w1" #[12] "TSRANGE 1925 1 1941 1" #[13] "EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1)+c4*time" #[14] "COEFF> c1 c2 c3 c4" #[15] "PDL> c3 1 3" #[16] "IDENTITY> y" #[17] "EQ> y = cn + i + g - t" #[18] "IDENTITY> p" #[19] "EQ> p = y - (w1+w2)" #[20] "IDENTITY> k" #[21] "EQ> k = TSLAG(k,1) + i" #[22] "IF> i > 0" #[23] "IDENTITY> k" #[24] "EQ> k = TSLAG(k,1)" #[25] "IF> i <= 0" #get endogenous and exogenous myModel$vendog #[1] "cn" "i" "w1" "y" "p" "k" myModel$vexog #[1] "w2" "t" "time" "g" #get behaviorals, identities and coefficients count myModel$totNumEqs #[1] 3 myModel$totNumIds #[1] 3 myModel$eqCoeffNum #[1] 12 #get the incidence matrix myModel$incidence_matrix # cn i w1 y p k #cn 0 0 1 0 1 0 #i 0 0 0 0 1 0 #w1 0 0 0 1 0 0 #y 1 1 0 0 0 0 #p 0 0 1 1 0 0 #k 0 1 0 0 0 0 #get the optimal reordering arrays myModel$vpre #NULL myModel$vblocks[[1]]$vsim #[1] "w1" "p" "i" "cn" "y" myModel$vblocks[[1]]$vfeed #[1] "y" myModel$vblocks[[1]]$vpost #[1] "k" #get the model max lag and the model name myModel$max_lag #[1] 3 myModel$modelName #myModelDefinition #get infos on behavioral w1 myModel$behaviorals$w1$eq #[1] "w1=c1+c2*(y+t-w2)+c3*TSLAG(y+t-w2,1)+c4*time" myModel$behaviorals$w1$eqCoefficientsNames #[1] "c1" "c2" "c3" "c3_PDL_1" "c3_PDL_2" "c4" myModel$behaviorals$w1$eqCoefficientsNamesOriginal #[1] "c1" "c2" "c3" "c4" myModel$behaviorals$w1$eqComponentsNames #[1] "t" "time" "w1" "w2" "y" myModel$behaviorals$w1$tsrange #[1] 1925 1 1941 1 myModel$behaviorals$w1$eqRegressorsNames #[1] "1" "(y+t-w2)" #[3] "TSLAG(y+t-w2,1)" "TSLAG(TSLAG(y+t-w2,1),1)" "TSLAG(TSLAG(y+t-w2,1),2)" "time" myModel$behaviorals$w1$eqRegressorsNamesOriginal #[1] "1" "(y+t-w2)" #[3] "TSLAG(y+t-w2,1)" "time" myModel$behaviorals$w1$pdlRaw #[1] "c3 1 3;" myModel$behaviorals$w1$pdlRestrictionMatrix # [,1] [,2] [,3] [,4] [,5] [,6] #[1,] 0 0 1 -2 1 0 #get infos on behavioral cn myModel$behaviorals$cn$errorRaw #[1] "AUTO(2)" myModel$behaviorals$cn$errorType #[1] "AUTO" myModel$behaviorals$cn$errorDim #[1] 2 myModel$behaviorals$cn$eqSimExp #expression(cn[4,]=cn__ADDFACTOR[4,]+cn__a1+cn__a2*p[4,]+cn__a3*(p[3,])+ #cn__a4*(w1[4,]+w2[4,])+cn__RHO_1*(cn[3,]-(cn__ADDFACTOR[3,]+ #cn__a1+cn__a2*p[3,]+cn__a3*(p[2,])+cn__a4*(w1[3,]+w2[3,])))+ #cn__RHO_2*(cn[2,]-(cn__ADDFACTOR[2,]+cn__a1+cn__a2*p[2,]+ #cn__a3*(p[1,])+cn__a4*(w1[2,]+w2[2,])))) #get infos on behavioral i myModel$behaviorals$i$matrixR # [,1] [,2] [,3] [,4] #[1,] 0 1 1 0 myModel$behaviorals$i$vectorR #[1] 1 myModel$behaviorals$i$restrictRaw #[1] "b2+b3=1;" #get infos on identitiy k myModel$identities$k$eqRaw #[1] "k=TSLAG(k,1)+i;k=TSLAG(k,1);" myModel$identities$k$ifRaw #[1] "i > 0;i <= 0;" myModel$identities$k$eqFull #[1] "__IF__ (i > 0) __THEN__ k=TSLAG(k,1)+i;__IF__ (i <= 0) __THEN__ k=TSLAG(k,1);" myModel$identities$k$eqComponentsNames #[1] "i" "k" myModel$identities$k$eqSimExp #expression(k[4,]=.MODEL_VIF(k[4,],i[4,] > 0,k_ADDFACTOR[4,]+ #(k[3,])+i[4,]),k[4,]=.MODEL_VIF(k[4,],i[4,] <= 0, #k_ADDFACTOR[4,]+(k[3,]))) myModel$identities$k$hasIF #[1] TRUE#define model myModelDefinition<- "MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment BEHAVIORAL> i TSRANGE 1923 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END" #load model myModel<-LOAD_MODEL(modelText=myModelDefinition) #retrieve model structure... #get definition myModel$cleanModel # [1] "BEHAVIORAL> cn" # [2] "TSRANGE 1925 1 1941 1" # [3] "EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2)" # [4] "COEFF> a1 a2 a3 a4" # [5] "ERROR> AUTO(2)" # [6] "BEHAVIORAL> i" # [7] "TSRANGE 1923 1 1941 1" # [8] "EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1)" # [9] "COEFF> b1 b2 b3 b4" #[10] "RESTRICT> b2 + b3 = 1" #[11] "BEHAVIORAL> w1" #[12] "TSRANGE 1925 1 1941 1" #[13] "EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1)+c4*time" #[14] "COEFF> c1 c2 c3 c4" #[15] "PDL> c3 1 3" #[16] "IDENTITY> y" #[17] "EQ> y = cn + i + g - t" #[18] "IDENTITY> p" #[19] "EQ> p = y - (w1+w2)" #[20] "IDENTITY> k" #[21] "EQ> k = TSLAG(k,1) + i" #[22] "IF> i > 0" #[23] "IDENTITY> k" #[24] "EQ> k = TSLAG(k,1)" #[25] "IF> i <= 0" #get endogenous and exogenous myModel$vendog #[1] "cn" "i" "w1" "y" "p" "k" myModel$vexog #[1] "w2" "t" "time" "g" #get behaviorals, identities and coefficients count myModel$totNumEqs #[1] 3 myModel$totNumIds #[1] 3 myModel$eqCoeffNum #[1] 12 #get the incidence matrix myModel$incidence_matrix # cn i w1 y p k #cn 0 0 1 0 1 0 #i 0 0 0 0 1 0 #w1 0 0 0 1 0 0 #y 1 1 0 0 0 0 #p 0 0 1 1 0 0 #k 0 1 0 0 0 0 #get the optimal reordering arrays myModel$vpre #NULL myModel$vblocks[[1]]$vsim #[1] "w1" "p" "i" "cn" "y" myModel$vblocks[[1]]$vfeed #[1] "y" myModel$vblocks[[1]]$vpost #[1] "k" #get the model max lag and the model name myModel$max_lag #[1] 3 myModel$modelName #myModelDefinition #get infos on behavioral w1 myModel$behaviorals$w1$eq #[1] "w1=c1+c2*(y+t-w2)+c3*TSLAG(y+t-w2,1)+c4*time" myModel$behaviorals$w1$eqCoefficientsNames #[1] "c1" "c2" "c3" "c3_PDL_1" "c3_PDL_2" "c4" myModel$behaviorals$w1$eqCoefficientsNamesOriginal #[1] "c1" "c2" "c3" "c4" myModel$behaviorals$w1$eqComponentsNames #[1] "t" "time" "w1" "w2" "y" myModel$behaviorals$w1$tsrange #[1] 1925 1 1941 1 myModel$behaviorals$w1$eqRegressorsNames #[1] "1" "(y+t-w2)" #[3] "TSLAG(y+t-w2,1)" "TSLAG(TSLAG(y+t-w2,1),1)" "TSLAG(TSLAG(y+t-w2,1),2)" "time" myModel$behaviorals$w1$eqRegressorsNamesOriginal #[1] "1" "(y+t-w2)" #[3] "TSLAG(y+t-w2,1)" "time" myModel$behaviorals$w1$pdlRaw #[1] "c3 1 3;" myModel$behaviorals$w1$pdlRestrictionMatrix # [,1] [,2] [,3] [,4] [,5] [,6] #[1,] 0 0 1 -2 1 0 #get infos on behavioral cn myModel$behaviorals$cn$errorRaw #[1] "AUTO(2)" myModel$behaviorals$cn$errorType #[1] "AUTO" myModel$behaviorals$cn$errorDim #[1] 2 myModel$behaviorals$cn$eqSimExp #expression(cn[4,]=cn__ADDFACTOR[4,]+cn__a1+cn__a2*p[4,]+cn__a3*(p[3,])+ #cn__a4*(w1[4,]+w2[4,])+cn__RHO_1*(cn[3,]-(cn__ADDFACTOR[3,]+ #cn__a1+cn__a2*p[3,]+cn__a3*(p[2,])+cn__a4*(w1[3,]+w2[3,])))+ #cn__RHO_2*(cn[2,]-(cn__ADDFACTOR[2,]+cn__a1+cn__a2*p[2,]+ #cn__a3*(p[1,])+cn__a4*(w1[2,]+w2[2,])))) #get infos on behavioral i myModel$behaviorals$i$matrixR # [,1] [,2] [,3] [,4] #[1,] 0 1 1 0 myModel$behaviorals$i$vectorR #[1] 1 myModel$behaviorals$i$restrictRaw #[1] "b2+b3=1;" #get infos on identitiy k myModel$identities$k$eqRaw #[1] "k=TSLAG(k,1)+i;k=TSLAG(k,1);" myModel$identities$k$ifRaw #[1] "i > 0;i <= 0;" myModel$identities$k$eqFull #[1] "__IF__ (i > 0) __THEN__ k=TSLAG(k,1)+i;__IF__ (i <= 0) __THEN__ k=TSLAG(k,1);" myModel$identities$k$eqComponentsNames #[1] "i" "k" myModel$identities$k$eqSimExp #expression(k[4,]=.MODEL_VIF(k[4,],i[4,] > 0,k_ADDFACTOR[4,]+ #(k[3,])+i[4,]),k[4,]=.MODEL_VIF(k[4,],i[4,] <= 0, #k_ADDFACTOR[4,]+(k[3,]))) myModel$identities$k$hasIF #[1] TRUE
This function verifies the input time series list and copies the data into a BIMETS model object. Provided time series must be BIMETS compliant, as defined in is.bimets
LOAD_MODEL_DATA(model=NULL, modelData=NULL, quietly=FALSE, ...)LOAD_MODEL_DATA(model=NULL, modelData=NULL, quietly=FALSE, ...)
model |
The BIMETS model object (see |
modelData |
The input time series list containing endogenous and exogenous data (see example). |
quietly |
If |
... |
Backward compatibility. |
This function add two new named element, i.e. modelData and frequency, into the output model object.
The new modelData element is a named list that contains all the input time series. Each element name of this list is set equal to the name of the endogenous or exogenous variable the time series data refer to.
The new frequency element is an integer that represent the frequency of the time series model data.
MDLLOAD_MODELESTIMATESIMULATESTOCHSIMULATEMULTMATRIXRENORMTIMESERIESBIMETS indexingBIMETS configuration
#define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #define model myModelDefinition<- "MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment BEHAVIORAL> i TSRANGE 1923 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END" #load model myModel<-LOAD_MODEL(modelText=myModelDefinition) #load data into the model myModel<-LOAD_MODEL_DATA(myModel,myModelData,showWarnings = TRUE) #Load model data "myModelData" into model "myModelDefinition"... #CHECK_MODEL_DATA(): warning, there are missing values in series "time". #...LOAD MODEL DATA OK #retrieve data from model object myModel$modelData$cn #Time Series: #Start = 1920 #End = 1941 #Frequency = 1 # [1] 39.8 41.9 45.0 49.2 50.6 52.6 55.1 56.2 57.3 #57.8 55.0 50.9 45.6 46.5 48.7 51.3 57.7 58.7 57.5 61.6 #[21] 65.0 69.7 myModel$modelData$w1 #Time Series: #Start = 1920 #End = 1941 #Frequency = 1 # [1] 28.8 25.5 29.3 34.1 33.9 35.4 37.4 37.9 39.2 #41.3 37.9 34.5 29.0 28.5 30.6 33.2 36.8 41.0 38.2 41.6 #[21] 45.0 53.3 myModel$modelData$i #Time Series: #Start = 1920 #End = 1941 #Frequency = 1 # [1] 2.7 -0.2 1.9 5.2 3.0 5.1 5.6 4.2 3.0 5.1 #1.0 -3.4 -6.2 -5.1 -3.0 -1.3 2.1 2.0 -1.9 1.3 #[21] 3.3 4.9 myModel$modelData$time #Time Series: #Start = 1920 #End = 1941 #Frequency = 1 # [1] NA -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 #0 1 2 3 4 5 6 7 8 9 10#define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #define model myModelDefinition<- "MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment BEHAVIORAL> i TSRANGE 1923 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END" #load model myModel<-LOAD_MODEL(modelText=myModelDefinition) #load data into the model myModel<-LOAD_MODEL_DATA(myModel,myModelData,showWarnings = TRUE) #Load model data "myModelData" into model "myModelDefinition"... #CHECK_MODEL_DATA(): warning, there are missing values in series "time". #...LOAD MODEL DATA OK #retrieve data from model object myModel$modelData$cn #Time Series: #Start = 1920 #End = 1941 #Frequency = 1 # [1] 39.8 41.9 45.0 49.2 50.6 52.6 55.1 56.2 57.3 #57.8 55.0 50.9 45.6 46.5 48.7 51.3 57.7 58.7 57.5 61.6 #[21] 65.0 69.7 myModel$modelData$w1 #Time Series: #Start = 1920 #End = 1941 #Frequency = 1 # [1] 28.8 25.5 29.3 34.1 33.9 35.4 37.4 37.9 39.2 #41.3 37.9 34.5 29.0 28.5 30.6 33.2 36.8 41.0 38.2 41.6 #[21] 45.0 53.3 myModel$modelData$i #Time Series: #Start = 1920 #End = 1941 #Frequency = 1 # [1] 2.7 -0.2 1.9 5.2 3.0 5.1 5.6 4.2 3.0 5.1 #1.0 -3.4 -6.2 -5.1 -3.0 -1.3 2.1 2.0 -1.9 1.3 #[21] 3.3 4.9 myModel$modelData$time #Time Series: #Start = 1920 #End = 1941 #Frequency = 1 # [1] NA -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 #0 1 2 3 4 5 6 7 8 9 10
This function returns the indices of the input TRUE elements. The input can be either an array or a time series. The result is usually used as a structured index to produce a new array.
LOCS(x=NULL, options='ALL', ...)LOCS(x=NULL, options='ALL', ...)
x |
This function accepts as input a boolean array or a boolean time series, often as the result of a logic comparison between an expression and a numerical array or a numerical time series: |
options |
A selection option can refine the result: |
... |
Backward compatibility. |
This function returns a numerical array built with the indices of the values that are TRUE in the input boolean array or in the input boolean time series.
NOELSis.bimetsBIMETS indexingTSERIESGETYEARPERIODNOELSNAMELISTINTSTSINFOTABITELIMELS
#create ts n<-10 ts1<-TSERIES((1:n),START=c(2000,1),FREQ=1) print(LOCS(ts1>7,options='FIRST')) #print 8 #generate error: print LOCS(): input has more than one TRUE element. tryCatch({print(LOCS(ts1>=3,options='UNIQUE'));},error=function(e){print(e$message);}) print(LOCS(is.na(c(1,2,NA,4,5,6,7,NA,NA)))) #print c(3,8,9)#create ts n<-10 ts1<-TSERIES((1:n),START=c(2000,1),FREQ=1) print(LOCS(ts1>7,options='FIRST')) #print 8 #generate error: print LOCS(): input has more than one TRUE element. tryCatch({print(LOCS(ts1>=3,options='UNIQUE'));},error=function(e){print(e$message);}) print(LOCS(is.na(c(1,2,NA,4,5,6,7,NA,NA)))) #print c(3,8,9)
BIMETS provides a language to unambiguously specify an econometric model. This page describes how to create a model and its general structure. The specification of an econometric model is translated and identified by keyword statements which are grouped in a model file, i.e. a plain text file or a character variable with a specific syntax. Collectively, these keyword statements constitute the BIMETS Model Description Language (from now on MDL). The model specifications consist of groups of statements. Each statement begins with a keyword. The keyword classifies the component of the model which is being specified.
Below is an example of a Klein's model with an MDL compliant syntax which can either be stored in a character variable or in a plain text file.
For more realistic scenarios, several advanced econometric exercises on the US Federal Reserve FRB/US econometric model (e.g., dynamic simulation in a monetary policy shock, rational expectations, endogenous targeting, stochastic simulation, etc.) are available in the "US Federal Reserve quarterly model (FRB/US) in R with bimets" vignette.
The content of the klein1.txt variable is:
R> klein1.txt=" MODEL COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1921 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END "
Please note that there are circular dependencies between equations of the model, e.g. p <- w1 <- y <- p as shown in the "BIMETS package" section figure in the pdf version of this reference manual. Circular dependencies imply that the model simulation must be solved with an iterative algorithm.
As shown, the model definition is quite intuitive. The first keyword is MODEL, while at the end of the model definition we can find the END keyword. Available tags in the definition of a generic BIMETS model are:
- EQUATION> or BEHAVIORAL> indicate the beginning of a series of keyword statements describing a behavioral equation. The behavioral statement general form is: BEHAVIORAL> name [TSRANGE startYear, startPeriod, endYear, endPeriod]
where name is the name of the behavioral equation and the optional TSRANGE specifies that the provided time interval must be used to estimate the coefficients. The optional TSRANGE is defined as a 4-dimensional numerical array built with starting year, starting period, ending year, and ending period.
Given , where are the historical values of the dependent variable and are the historical values of the regressors, if the requested estimation method is OLS (Ordinary Least Squares), in the general case (i.e. no restrictions nor error auto-correlation, as described later) the coefficients will be calculated as: .
If the requested estimation method is IV (Instrumental Variables), given the matrix built with instrumental variables as columns , that should not be correlated to the disturbance terms, i.e. , the coefficients will be either calculated as , or more generally as: where and ,
- IDENTITY> indicates the beginning of a series of keyword statements describing an identity or technical equation. The identity statement general form is: IDENTITY> name
where name is the identity name.
- EQ> specifies the mathematical expression for a behavioral or an identity equation.
The equation statement general form for a behavioral equation is:EQ> LHS = coeff1*f1 + coeff2*f2 + coeff3*f3 + ...
where LHS is a function of the behavioral variable, coeff1, coeff2, coeff3, ... are the coefficient names of the equation and f1, f2, f3, ... are functions of variables.
The equation statement general form for an identity equation is:EQ> LHS = f1 + f2 + f3 + ...
where LHS is a function of the identity variable and f1, f2, f3, ... are functions of variables.
The following MDL functions can be used in the LHS left-hand side of the equation, with name as the name of the behavioral or the identity variable:
- name - i.e. the identity function;
- TSDELTA(name,i) - i-periods difference of the name time series;
- TSDELTAP(name,i) - i-periods percentage difference of the name time series;
- TSDELTALOG(name,i) - i-periods logarithmic difference of the name time series;
- LOG(name) - log of the name time series;
- EXP(name) - exponential of the name time series.
On the other side, the mathematical expression available for use in the RHS right-hand side of the EQ> equation and in the IV> expression described later in this page (i.e. f1, f2, f3, ...) can include the standard arithmetic operators, parentheses and the following MDL functions:
- TSLAG(ts,i) - lag the ts time series by i-periods;
- TSLEAD(ts,i) - lead the ts time series by i-periods;
- TSDELTA(ts,i) - i-periods difference of the ts time series;
- TSDELTAP(ts,i) - i-periods percentage difference of the ts time series;
- TSDELTALOG(ts,i) - i-periods logarithmic difference of the ts time series;
- MOVAVG(ts,i) - i-periods moving average of the ts time series;
- MOVSUM(ts,i) - i-periods moving sum of the ts time series;
- LOG(ts) - log of the ts time series;
- EXP(ts) - exponential of the ts time series;
- ABS(ts) - absolute values of the ts time series.
Note that BIMETS classifies a model as a forward-looking model if any model equation contains the TSLEAD time series function. More details about forward-looking models are available in the "Rational Expectations Models" section of the SIMULATE help pages.MDL function names are reserved names. They cannot be used as variable or coefficient names. The coefficient names are specified in a subsequent COEFF> keyword statement within a behavioral equation. By definition, identities do not have any coefficient that must be assessed. Any name not specified as a coefficient name or mentioned on the list of the available MDL functions is assumed to be a variable.
- COEFF> specifies the coefficient names used in the EQ> keyword statement of a behavioral equation. The coefficients statement general form is:COEFF> coeff0 coeff1 coeff2 ... coeffn.
The coefficients order in this statement must be the same as it appears in the behavioral equation.
- ERROR> specifies an autoregressive process of a given order for the regression error. The error statement general form is:ERROR> AUTO(n)
where n is the order of the autoregressive process for the error.
During an estimation, users must ensure that the required data are available for the specified error structure: n periods of data before the time interval specified by TSRANGE must be defined in any time series involved in the regression.
The solution requires an iterative algorithm. Given , where are the historical values of the dependent variable and are the historical values of the regressors, the iterative algorithm is based on the Cochrane-Orcutt procedure:
1) Make an initial estimation by using the original TSRANGE extended backward n periods (given n as the autocorrelation order).
2) Estimate the error autocorrelation coefficients with by regressing the residuals on their lagged values by using the auxiliary model:
3) Transform the data for the dependent and the independent variables by using the estimated . The new dependent variable will be: , and the new independent variables will be with the matrix defined as:
4) Run another estimation on the original model by using the suitable TSRANGE and the transformed data coming out of step 3 and compute the new time series for the residuals.
5) Estimate the new autocorrelation coefficients , by regressing the new residuals arising from step 4 (similar to step 2)
6) Carry out the convergence check through a comparison among the previous and the new ones arising from steps 5.
If , where is the vector at the iteration and is a small convergence factor, then exit otherwise repeat from step 3 with i <- i+1.
- RESTRICT> is a keyword that can be used to specify linear coefficient restrictions. A deterministic restriction can be applied to any equation coefficient. Any number of RESTRICT> keywords is allowed for each behavioral equation.
A deterministic (exact) coefficient restriction sets a linear expression containing one or more coefficients equal to a constant. The restriction only affects the coefficients of the behavioral equation in which it is specified. The restriction statement general form is:
RESTRICT> linear_combination_of_coefficients_1 = value_1 ... linear_combination_of_coefficients_n = value_n
where linear_combination_of_coefficients_i, i=1..n is a linear combination of the coefficient(s) to be restricted and value_i is the in-place scalar value to which the linear combination of the coefficients is set equal. Each linear combination can be set equal to a different value.MDL example:
RESTRICT> coeff1 = 0 coeff2 = 10.5 coeff3-3*coeff4+1.2*coeff5 = 0
In many econometric packages, linear restrictions have to be coded by hand in the equations. BIMETS allows users to write down the restriction in a natural way, thus applying a constrained minimization. This procedure, although it leads to approximate numerical estimates, allows an easy implementation.
The theory behind this procedure is that of the Lagrange multipliers. Presented here is an example of its implementation.
Suppose that we have an equation defined as:
EQUATION> Y TSRANGE 2010 1 2015 4 EQ> Y = C1*X1 + C2*X2 + C3*X3 COEFF> C1 C2 C3 RESTRICT> 1.1*C1 + 1.3*C3 = 2.1 1.2*C2 = 0.8
Coefficients C1, C2, C3 are to be estimated. They are subject to the linear constraints specified by the RESTRICT> keyword statement. In the case of OLS estimation, this is carried out in the following steps:
1) Compute the cross-product matrices and where is a matrix with dimension [NOBS x NREG] containing the values of the independent variables (regressors) historical observations (and a vector of ones for the constant term, if any), and where is a NOBS elements vector of the dependent variable (regressand) historical observations; NOBS is the number of observations available on the TSRANGE specified in the behavioral equation, and NREG is the number of regressors, or coefficients;
2) Build the restriction matrices. In the example:
and
R is a matrix of [NRES x NREG] size, and r is a vector of [NRES] length, where NRES is the number of restrictions;
3) Compute the scaling factors for the augmentation to be performed in the next step:
where is the i-th row of the R matrix.
Assuming , in the example above we will have:
The augmented matrices will then be defined as:
and
4) Compute the so-called "augmented" cross-product matrix by adding to the cross-product matrix a total of NRES rows and NRES columns:
5) Similarly, compute the so-called "augmented" cross-product matrix by adding a total of NRES elements to the cross-product matrix :
6) Calculate the augmented coefficients by regressing the on the .
The first NREG values of the augmented coefficients array are the estimated coefficients with requested restrictions. The last NRES values are the errors we have on the deterministic restrictions.
In the case of IV estimation, the procedure is the same as in the OLS case, but the matrix has to be replaced with the matrix , as previously defined in the BEHAVIORAL> keyword.
- PDL> is a keyword that defines an Almon polynomial distributed lag to be used in estimation. Almon Polynomial distributed lags are specific kind of deterministic restrictions imposed on the coefficients of the distributed lags of a specific regressor. Multiple PDLs on a single behavioral equation can be defined.
The PDL> statement general form is:PDL> coeffname degree laglength [N] [F]
where coeffname is the name of a coefficient, degree is an integer scalar specifying the degree of the polynomial, laglength is an integer scalar specifying the length of the polynomial (in number of time periods), the optional N (i.e. "nearest") means that the nearest lagged term of the expansion, i.e., the first term, is restricted to zero, and the optional F (i.e. "farthest") means that the farthest lagged term of the expansion, i.e., the last term, is restricted to zero; the PDL> keyword statement thusly defined applies an Almon polynomial distributed lag to the regressor associated with the coeffname coefficient, of laglength length and degree degree, by providing the appropriate expansion and the deterministic restrictions for the degree and length specified. These expansions are not explicitly shown to the user, i.e., the original model is not changed.laglength must be greater than degree (see example below).
A PDL term can be further referenced in a RESTRICT> keyword statement by using the following syntax: LAG(coefname, pdllag).
Example: RESTRICT> LAG(coeff2,3) = 0 means that, during the estimation, the regressor related to the coefficient coeff2 and lagged by 3 periods in the PDL expansion must have a coefficient equal to zero. This example also implies that a PDL> coeff2 x y with y > 3 has been declared in the same behavioral.
The implementing rules are the following:
1) Read off the laglength of the PDL keyword and expand the column of the regressor related to coeffname in the matrix X (i.e. the original regressors matrix) with the lagged values of the regressor, from left to right, starting form the lag 1 to the lag laglength-1. The matrix X will now have a [NOBS x (NREG+laglength-1)] size, with NOBS as the number of observations in the specified TSRANGE and NREG as the number of regressors, or coefficients.
2) Build the restriction matrix R with the following [ Nrow x Ncol ] dimensions:Nrow = laglength - ( degree + 1 )Ncol = NREG + laglength - 1
This matrix's elements will be zero except for the (laglength)-columns related to the section of the expanded columns in the X matrix. For every row we will have to insert degree+2 numbers different from zero.
The degree+2 numbers are taken form the Tartaglia's-like triangle:
1 -2 1 1 -3 3 -1 1 -4 6 -4 1 1 -5 10 -10 5 1 ... ... ... ...
where in the i-th row we find the numbers for a PDL of degree=i.
The r vector giving the knows terms for the restrictions is a vector ofNRES = laglength - (degree + 1) elements equal to zero.
An example will clarify:
EQUATION> Y TSRANGE 2010 1 2015 4 EQ> Y = C1*X1 + C2*X2 + C3*X3 COEFF> C1 C2 C3 PDL> C2 2 5
then
and
The expanded regressors are:X1, X2, TSLAG(X2,1), TSLAG(X2,2), TSLAG(X2,3), TSLAG(X2,4), X3.
The scaling factor is given, as in the standard restriction case, by:
- IF> keyword is used to conditionally evaluate an identity during a simulation, depending on a logical expression's value. Thus, it is possible to have a model alternating between two or more identity specifications for each simulation period, depending upon results from other equations.
The IF> statement general form is:IF> logical_expression
The IF> keyword must be specified within an identity group; this keyword causes the equation specified in the identity group to be evaluated during the current simulation period only when the logical_expression is TRUE.
Only one IF> keyword is allowed in an identity group. Further occurrences produce an error message, and processing stops.
The logical_expression can be composed of constants, endogenous variables, exogenous variables, an expression among variables, combinations of the logical operators; mathematical operators and the MDL functions listed in the EQ> section are allowed.
In the following MDL example, the value of the endogenous myIdentity variable is specified with two complementary conditional identities, depending on the TSDELTA() result:
IDENTITY> myIdentity IF> TSDELTA(myEndog*(1-myExog)) > 0 EQ> myIdentity = TSLAG(myIdentity)+1 IDENTITY> myIdentity IF> TSDELTA(myEndog*(1-myExog)) <= 0 EQ> myIdentity = TSLAG(myIdentity)
- IV> specifies the mathematical expression for an instrumental variable used in a behavioral equation.
The general form for an instrumental variable expression is:IV> f1 + f2 + f3 + ... f1, f2, f3, ... are functions of variables.
The mathematical expression available for use in the IV> definition are those already described in the EQ> section.
- COMMENT> can be used to insert comments into a model. The general form of this keyword is:COMMENT> text
The text following the COMMENT> keyword is ignored during all processing and must lie in the same line. Comments cannot be inserted within another keyword statement. A dollar sign in the first position of a line is equivalent to using the COMMENT> keyword, as in this exmaple:
$This is a comment
No other keywords are currently allowed in the MDL syntax.
LOAD_MODELESTIMATESIMULATESTOCHSIMULATEMULTMATRIXRENORMOPTIMIZETIMESERIESBIMETS indexingBIMETS configurationsummary
######################################################### #KLEIN MODEL WITH AUTOCORRELATION, RESTRICTIONS AND #CONDITIONAL EVALUATIONS #define model myModel<- "MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> Consumption with autocorrelation on errors BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment with restrictions BEHAVIORAL> i TSRANGE 1923 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor with PDL BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 2 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END" #define model data modelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data model<-LOAD_MODEL(modelText=myModel) model<-LOAD_MODEL_DATA(model,modelData) #estimate model model<-ESTIMATE(model) #simulate model model<-SIMULATE(model ,TSRANGE=c(1923,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ) ######################################################### #KLEIN MODEL WITH LHS FUNCTIONS #define the model with LHS funs myModel<-'MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> LHS functions on EQ COMMENT> Exp Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> EXP(cn) = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Log Investment BEHAVIORAL> i TSRANGE 1925 1 1941 1 EQ> LOG(i) = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(TSDELTA(y)+t-w2) + c3*TSLAG(TSDELTA(y)+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Delta Gross National Product IDENTITY> y EQ> TSDELTA(y) = EXP(cn) + LOG(i) + g - t COMMENT> Profits IDENTITY> p EQ> p = TSDELTA(y) - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + LOG(i) IF> LOG(i) > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> LOG(i) <= 0 END' #define model data modelData<-list( cn=TSERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3, 57.8,55,50.9,45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g=TSERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4, 10.7,10.2,9.3,10,10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i=TSERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4, -6.2,-5.1,-3,-1.3,2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k=TSERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4, 207.6,210.6,215.7,216.7,213.3,207.1,202, 199,197.7,199.8,201.8,199.9,201.2,204.5,209.4, START=c(1920,1),FREQ=1), p=TSERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1, 21.7,15.6,11.4,7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1=TSERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2, 41.3,37.9,34.5,29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y=TSERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67, 57.7,50.7,41.3,45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t=TSERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5, 8.3,5.4,6.8,7.2,8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time=TSERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2, 3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2=TSERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2, 4.8,5.3,5.6,6,6.1,7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #example data transformation modelData<-within(modelData,{ i=exp(i); #we have LOG(i) in the model MDL definition cn=log(cn); #we have EXP(cn) in the model MDL definition y=CUMSUM(y) #we have TSDELTA(y) in the model MDL definition }) #load model and model data model<-LOAD_MODEL(modelText=myModel) model<-LOAD_MODEL_DATA(model,modelData) #estimate model model<-ESTIMATE(model) #simulate model model<-SIMULATE(model ,TSRANGE=c(1925,1,1930,1) ,simConvergence=0.00001 ,simIterLimit=100 ) ######################################################### #SIMPLE MODEL WITH IV #define the model with IVs myShortModelDefinition<-" MODEL COMMENT> Consumption with IV BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 IV> 1 IV> TSLAG(y) IV> TSLAG(w1)*pi+0.5 IV> exp(w2) END " #load model myShortModel<-LOAD_MODEL(modelText=myShortModelDefinition)######################################################### #KLEIN MODEL WITH AUTOCORRELATION, RESTRICTIONS AND #CONDITIONAL EVALUATIONS #define model myModel<- "MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> Consumption with autocorrelation on errors BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment with restrictions BEHAVIORAL> i TSRANGE 1923 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor with PDL BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 2 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END" #define model data modelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data model<-LOAD_MODEL(modelText=myModel) model<-LOAD_MODEL_DATA(model,modelData) #estimate model model<-ESTIMATE(model) #simulate model model<-SIMULATE(model ,TSRANGE=c(1923,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ) ######################################################### #KLEIN MODEL WITH LHS FUNCTIONS #define the model with LHS funs myModel<-'MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> LHS functions on EQ COMMENT> Exp Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> EXP(cn) = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Log Investment BEHAVIORAL> i TSRANGE 1925 1 1941 1 EQ> LOG(i) = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(TSDELTA(y)+t-w2) + c3*TSLAG(TSDELTA(y)+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Delta Gross National Product IDENTITY> y EQ> TSDELTA(y) = EXP(cn) + LOG(i) + g - t COMMENT> Profits IDENTITY> p EQ> p = TSDELTA(y) - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + LOG(i) IF> LOG(i) > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> LOG(i) <= 0 END' #define model data modelData<-list( cn=TSERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3, 57.8,55,50.9,45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g=TSERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4, 10.7,10.2,9.3,10,10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i=TSERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4, -6.2,-5.1,-3,-1.3,2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k=TSERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4, 207.6,210.6,215.7,216.7,213.3,207.1,202, 199,197.7,199.8,201.8,199.9,201.2,204.5,209.4, START=c(1920,1),FREQ=1), p=TSERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1, 21.7,15.6,11.4,7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1=TSERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2, 41.3,37.9,34.5,29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y=TSERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67, 57.7,50.7,41.3,45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t=TSERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5, 8.3,5.4,6.8,7.2,8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time=TSERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2, 3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2=TSERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2, 4.8,5.3,5.6,6,6.1,7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #example data transformation modelData<-within(modelData,{ i=exp(i); #we have LOG(i) in the model MDL definition cn=log(cn); #we have EXP(cn) in the model MDL definition y=CUMSUM(y) #we have TSDELTA(y) in the model MDL definition }) #load model and model data model<-LOAD_MODEL(modelText=myModel) model<-LOAD_MODEL_DATA(model,modelData) #estimate model model<-ESTIMATE(model) #simulate model model<-SIMULATE(model ,TSRANGE=c(1925,1,1930,1) ,simConvergence=0.00001 ,simIterLimit=100 ) ######################################################### #SIMPLE MODEL WITH IV #define the model with IVs myShortModelDefinition<-" MODEL COMMENT> Consumption with IV BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 IV> 1 IV> TSLAG(y) IV> TSLAG(w1)*pi+0.5 IV> exp(w2) END " #load model myShortModel<-LOAD_MODEL(modelText=myShortModelDefinition)
This function returns a monthly (dis)aggregated time series, by using as input an annual, semiannual, quarterly or daily time series.
MONTHLY(x = NULL, fun = NULL, avoidCompliance = FALSE, ...)MONTHLY(x = NULL, fun = NULL, avoidCompliance = FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
fun |
Only for daily input time series: |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a monthly BIMETS time series.
YEARLYSEMIANNUALQUARTERLYDAILY
#TS FREQ 2 SEMIANNUAL TO MONTHLY ts1<-TSERIES((1:10),START=c(2000,1),FREQ=2) TABIT(MONTHLY(ts1,fun='INTERP_CENTER')) #TS DAILY TO MONTHLY ts1<-TSERIES((1:366),START=c(2000,1),FREQ='D') TABIT(MONTHLY(ts1,fun='STOCK'))#TS FREQ 2 SEMIANNUAL TO MONTHLY ts1<-TSERIES((1:10),START=c(2000,1),FREQ=2) TABIT(MONTHLY(ts1,fun='INTERP_CENTER')) #TS DAILY TO MONTHLY ts1<-TSERIES((1:366),START=c(2000,1),FREQ='D') TABIT(MONTHLY(ts1,fun='STOCK'))
This function returns the moving average of the elements of the input array or the input time series. The result is an object of the same class of the input, and its elements are the moving average of length L of the input values. If the input is a time series, the DIRECTION of the moving average, i.e backward, forward or centered, can be provided. MAVE is an alias for MOVAVG
MOVAVG(x = NULL, L = NULL, DIRECTION = NULL, ignoreNA=FALSE, avoidCompliance = FALSE, ...) MAVE(x = NULL, L = NULL, DIRECTION = NULL, ignoreNA=FALSE, avoidCompliance = FALSE, ...)MOVAVG(x = NULL, L = NULL, DIRECTION = NULL, ignoreNA=FALSE, avoidCompliance = FALSE, ...) MAVE(x = NULL, L = NULL, DIRECTION = NULL, ignoreNA=FALSE, avoidCompliance = FALSE, ...)
x |
Input numerical array or time series that must satisfy the compliance control check defined in |
L |
Length of the mean. Must be a positive integer. |
DIRECTION |
if |
ignoreNA |
Ignore missing values. |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns an object of the same class of the input, i.e. an array or a BIMETS time series.
TSDELTATSLAGTSPROJECTTSEXTENDTSLEADCUMSUMINDEXNUMVERIFY_MAGNITUDEGETRANGE
#input data inputArray<-c(1,2,3,4,NA,1,2,3,4,5) #array lag 3 out_movavg<-MOVAVG(inputArray,3) print(out_movavg) #ts lag 4 centered with missings ts1<-TSERIES(inputArray,START=c(2000,1),FREQ='A') out_movavg<-MAVE(ts1,4,'CENTER') TABIT(out_movavg) #ts daily ts1<-TSERIES(inputArray,START=c(2000,1),FREQ='D') out_movavg<-MAVE(ts1,3) TABIT(ts1,out_movavg)#input data inputArray<-c(1,2,3,4,NA,1,2,3,4,5) #array lag 3 out_movavg<-MOVAVG(inputArray,3) print(out_movavg) #ts lag 4 centered with missings ts1<-TSERIES(inputArray,START=c(2000,1),FREQ='A') out_movavg<-MAVE(ts1,4,'CENTER') TABIT(out_movavg) #ts daily ts1<-TSERIES(inputArray,START=c(2000,1),FREQ='D') out_movavg<-MAVE(ts1,3) TABIT(ts1,out_movavg)
This function returns the moving sum of the elements of the input array or the input time series. The result is an object of the same class of the input, and its elements are the moving sum of length L of the input values. If the input is a time series, the DIRECTION of the moving sum, i.e backward, forward or centered, can be provided. MTOT and MSUM are alias for MOVTOT and MOVSUM
MOVSUM(x = NULL, L = NULL, DIRECTION = NULL, ignoreNA=FALSE, avoidCompliance = FALSE, ...) MOVTOT(x = NULL, L = NULL, DIRECTION = NULL, ignoreNA=FALSE, avoidCompliance = FALSE, ...)MOVSUM(x = NULL, L = NULL, DIRECTION = NULL, ignoreNA=FALSE, avoidCompliance = FALSE, ...) MOVTOT(x = NULL, L = NULL, DIRECTION = NULL, ignoreNA=FALSE, avoidCompliance = FALSE, ...)
x |
Input numerical array or time series that must satisfy the compliance control check defined in |
L |
Length of the sum. It must be a positive integer. |
DIRECTION |
if |
ignoreNA |
Ignore missing values. |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns an object of the same class of the input, i.e. an array or a BIMETS time series.
TSDELTATSLAGTSPROJECTTSEXTENDTSLEADCUMSUMINDEXNUMVERIFY_MAGNITUDEGETRANGE
#input data inputArray<-c(1,2,3,4,NA,1,2,3,4,5) #array lag 3 out_movtot<-MOVSUM(inputArray,3) print(out_movtot) #ts lag 4 centered with missings ts1<-TSERIES(inputArray,START=c(2000,1),FREQ='A') out_movtot<-MOVSUM(ts1,4,'CENTER') TABIT(out_movtot) #ts daily ts1<-TSERIES(inputArray,START=c(2000,1),FREQ='D') out_movtot<-MSUM(ts1,3) TABIT(ts1,out_movtot)#input data inputArray<-c(1,2,3,4,NA,1,2,3,4,5) #array lag 3 out_movtot<-MOVSUM(inputArray,3) print(out_movtot) #ts lag 4 centered with missings ts1<-TSERIES(inputArray,START=c(2000,1),FREQ='A') out_movtot<-MOVSUM(ts1,4,'CENTER') TABIT(out_movtot) #ts daily ts1<-TSERIES(inputArray,START=c(2000,1),FREQ='D') out_movtot<-MSUM(ts1,3) TABIT(ts1,out_movtot)
This function computes the matrix of both impact and interim multipliers, for a selected set of endogenous variables (i.e. TARGET) with respect to a selected set of exogenous variables (i.e. INSTRUMENT), by subtracting the results from different simulations in each period of the provided time range (i.e. TSRANGE). The simulation algorithms are the same as those used for the SIMULATE operation.
The MULTMATRIX procedure is articulated as follows:
1- simultaneous simulations are done;
2- the first simulation establishes the base line solution (without shocks);
3- the other simulations are done with shocks applied to each of the INSTRUMENT one at a time for every period in TSRANGE;
4- each simulation follows the defaults described in the SIMULATE help page, but has to be STATIC for the IMPACT multipliers and DYNAMIC for INTERIM multipliers;
5- given MM_SHOCK shock amount as a very small positive number, derivatives are computed by subtracting the base line solution of the TARGET from the shocked solution, then dividing by the value of the base line INSTRUMENT time the MM_SHOCK.
The IMPACT multipliers measure the effects of impulse exogenous changes on the endogenous variables in the same time period. They can be defined as partial derivatives of each current endogenous variable with respect to each current exogenous variable, all other exogenous variables being kept constant.
Given an endogenous variable at time and an exogenous variable at time the impact multiplier is defined as and can be approximated by , with the values fo the simulated endogenous variable at time when is shocked to
The INTERIM or delay-r multipliers measure the delay-r effects of impulse exogenous changes on the endogenous variables in the same time period. The delay-r multipliers of the endogenous variable Y with respect to the exogenous variable X related to a dynamic simulation from time t to time t+r can be defined as the partial derivative of the current endogenous variable Y at time t+r with respect to the exogenous variable X at time t, all other exogenous variables being kept constant.
Given an endogenous variable at time and an exogenous variable at time the impact interim or delay-r multiplier is defined as and can be approximated by , with the values fo the simulated endogenous variable at time when is shocked to
Users can also declare an endogenous variable as the INSTRUMENT variable. In this case, the constant adjustment (see SIMULATE) related to the provided endogenous variable will be used as the INSTRUMENT exogenous variable (see example);
MULTMATRIX(model=NULL, simAlgo='GAUSS-SEIDEL', TSRANGE=NULL, simType='DYNAMIC', simConvergence=0.01, simIterLimit=100, ZeroErrorAC=FALSE, BackFill=0, Exogenize=NULL, ConstantAdjustment=NULL, verbose=FALSE, verboseSincePeriod=0, verboseVars=NULL, TARGET=NULL, INSTRUMENT=NULL, MM_SHOCK=0.00001, quietly=FALSE, JACOBIAN_SHOCK=1e-4, JacobianDrop=NULL, forceForwardLooking=FALSE, avoidCompliance=FALSE, ...)MULTMATRIX(model=NULL, simAlgo='GAUSS-SEIDEL', TSRANGE=NULL, simType='DYNAMIC', simConvergence=0.01, simIterLimit=100, ZeroErrorAC=FALSE, BackFill=0, Exogenize=NULL, ConstantAdjustment=NULL, verbose=FALSE, verboseSincePeriod=0, verboseVars=NULL, TARGET=NULL, INSTRUMENT=NULL, MM_SHOCK=0.00001, quietly=FALSE, JACOBIAN_SHOCK=1e-4, JacobianDrop=NULL, forceForwardLooking=FALSE, avoidCompliance=FALSE, ...)
model |
see |
simAlgo |
see |
TSRANGE |
see |
simType |
see |
simConvergence |
see |
simIterLimit |
see |
ZeroErrorAC |
see |
BackFill |
see |
Exogenize |
see |
ConstantAdjustment |
see |
verbose |
see |
verboseSincePeriod |
see |
verboseVars |
see |
TARGET |
A |
INSTRUMENT |
A |
MM_SHOCK |
The value of the shock added to |
quietly |
see |
JACOBIAN_SHOCK |
see |
JacobianDrop |
see |
forceForwardLooking |
see |
avoidCompliance |
see |
... |
see |
This function will add a new element named MultiplierMatrix into the output BIMETS model object.
The new MultiplierMatrix element is a (NumPeriods * Nendogenous) X (NumPeriods * Nexogenous) matrix,
with NumPeriods as the number of periods specified in the TSRANGE, Nendogeous the count of the endogenous variables in the TARGET array and Nexogenous the count of the exogenous variables in the INSTRUMENT array.
The arguments passed to the function call during the latest MULTMATRIX run will be inserted into the '__SIM_PARAMETERS__' element of the model simulation list (see SIMULATE); this data can be helpful in order to replicate the multiplier matrix results.
Row and column names in the output multiplier matrix identify the variables and the periods involved in the derivative solution, with the syntax VARIABLE_PERIOD (see example).
MDLLOAD_MODELESTIMATESIMULATESTOCHSIMULATERENORMTIMESERIESBIMETS indexingBIMETS configuration
#define model myModelDefinition<- "MODEL COMMENT> Klein Model 1 of the U.S. Economy COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1921 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data myModel<-LOAD_MODEL(modelText=myModelDefinition) myModel<-LOAD_MODEL_DATA(myModel,myModelData) #estimate model myModel<-ESTIMATE(myModel) #calculate impact multipliers of Government Expenditure 'g' and #Government Wage Bill 'w2' with respect of Consumption 'cn' and #Gross National Product 'y' in the Klein model on the year 1941: myModel<-MULTMATRIX(myModel, symType='STATIC', TSRANGE=c(1941,1,1941,1), INSTRUMENT=c('w2','g'), TARGET=c('cn','y')) #Multiplier Matrix: 100.00% #...MULTMATRIX OK print(myModel$MultiplierMatrix) # w2_1 g_1 #cn_1 0.4540346 1.671956 #y_1 0.2532000 3.653260 #Results show that the impact multiplier of "y" #with respect to "g" is +3.65 #If we change Government Expenditure 'g' value in 1941 #from 22.3 (its historical value) to 23.3 (+1) #then the simulated Gross National Product "y" #in 1941 changes from 95.2 to 99, #thusly roughly confirming the +3.65 impact multiplier. #Note that "g" appears only once in the model definition, and only #in the "y" equation, with a coefficient equal to one. (Keynes would approve) #multi-period interim multipliers myModel<-MULTMATRIX(myModel, TSRANGE=c(1940,1,1941,1), INSTRUMENT=c('w2','g'), TARGET=c('cn','y')) #output multipliers matrix (note the zeros when the period #of the INSTRUMENT is greater than the period of the TARGET) print(myModel$MultiplierMatrix) # w2_1 g_1 w2_2 g_2 #cn_1 0.4478202 1.582292 0.0000000 0.000000 #y_1 0.2433382 3.510971 0.0000000 0.000000 #cn_2 -0.3911001 1.785042 0.4540346 1.671956 #y_2 -0.6251177 2.843960 0.2532000 3.653260 #multiplier matrix with endogenous variable 'w1' as instrument #note the ADDFACTOR suffix in the column name, referring to the #constant adjustment of the endogneous 'w1' myModel<-MULTMATRIX(myModel, TSRANGE=c(1940,1,1941,1), INSTRUMENT=c('w2','w1'), TARGET=c('cn','y')) #Multiplier Matrix: 100.00% #...MULTMATRIX OK myModel$MultiplierMatrix # w2_1 w1_ADDFACTOR_1 w2_2 w1_ADDFACTOR_2 #cn_1 0.4478202 0.7989328 0.0000000 0.0000000 #y_1 0.2433382 0.4341270 0.0000000 0.0000000 #cn_2 -0.3911001 -0.4866248 0.4540346 0.8100196 #y_2 -0.6251177 -0.9975073 0.2532000 0.4517209#define model myModelDefinition<- "MODEL COMMENT> Klein Model 1 of the U.S. Economy COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1921 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data myModel<-LOAD_MODEL(modelText=myModelDefinition) myModel<-LOAD_MODEL_DATA(myModel,myModelData) #estimate model myModel<-ESTIMATE(myModel) #calculate impact multipliers of Government Expenditure 'g' and #Government Wage Bill 'w2' with respect of Consumption 'cn' and #Gross National Product 'y' in the Klein model on the year 1941: myModel<-MULTMATRIX(myModel, symType='STATIC', TSRANGE=c(1941,1,1941,1), INSTRUMENT=c('w2','g'), TARGET=c('cn','y')) #Multiplier Matrix: 100.00% #...MULTMATRIX OK print(myModel$MultiplierMatrix) # w2_1 g_1 #cn_1 0.4540346 1.671956 #y_1 0.2532000 3.653260 #Results show that the impact multiplier of "y" #with respect to "g" is +3.65 #If we change Government Expenditure 'g' value in 1941 #from 22.3 (its historical value) to 23.3 (+1) #then the simulated Gross National Product "y" #in 1941 changes from 95.2 to 99, #thusly roughly confirming the +3.65 impact multiplier. #Note that "g" appears only once in the model definition, and only #in the "y" equation, with a coefficient equal to one. (Keynes would approve) #multi-period interim multipliers myModel<-MULTMATRIX(myModel, TSRANGE=c(1940,1,1941,1), INSTRUMENT=c('w2','g'), TARGET=c('cn','y')) #output multipliers matrix (note the zeros when the period #of the INSTRUMENT is greater than the period of the TARGET) print(myModel$MultiplierMatrix) # w2_1 g_1 w2_2 g_2 #cn_1 0.4478202 1.582292 0.0000000 0.000000 #y_1 0.2433382 3.510971 0.0000000 0.000000 #cn_2 -0.3911001 1.785042 0.4540346 1.671956 #y_2 -0.6251177 2.843960 0.2532000 3.653260 #multiplier matrix with endogenous variable 'w1' as instrument #note the ADDFACTOR suffix in the column name, referring to the #constant adjustment of the endogneous 'w1' myModel<-MULTMATRIX(myModel, TSRANGE=c(1940,1,1941,1), INSTRUMENT=c('w2','w1'), TARGET=c('cn','y')) #Multiplier Matrix: 100.00% #...MULTMATRIX OK myModel$MultiplierMatrix # w2_1 w1_ADDFACTOR_1 w2_2 w1_ADDFACTOR_2 #cn_1 0.4478202 0.7989328 0.0000000 0.0000000 #y_1 0.2433382 0.4341270 0.0000000 0.0000000 #cn_2 -0.3911001 -0.4866248 0.4540346 0.8100196 #y_2 -0.6251177 -0.9975073 0.2532000 0.4517209
In the case of strings input, this function returns a string array built with the input strings. In the case of time series input, this function returns a list built with the input time series; the output list names will be the variable names passed as arguments.
NAMELIST(...)NAMELIST(...)
... |
List of strings or list of time series. In the case of a list of strings, if an input string is not eligible to be a variable name, e.g. a string composed only with numbers, or with special characters, a warning will be thrown and a message will describe the required change made to the input string in order to make it eligible to be a variable name (see example). |
In the case of strings as input, this function returns a string array built with the input strings. In the case of time series as input, this function returns a list built with the input time series; the output list names will be the variable names passed as arguments.
NOELSis.bimetsBIMETS indexingTSERIESGETYEARPERIODLOCS
#NAMELIST with time series... ts1<-TSERIES(1:10,START=c(2000,1),FREQ=12) ts2<-TSERIES(10:20,START=c(2002,5),FREQ=12) myNameList<-NAMELIST(ts1,ts2) print(myNameList) #prints a list with $ts1 and $ts2 elements #please note that names are 'ts1' and 'ts2'... #$ts1 # Jan Feb Mar Apr May Jun Jul Aug Sep Oct #2000 1 2 3 4 5 6 7 8 9 10 #$ts2 # Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec #2002 10 11 12 13 14 15 16 17 #2003 18 19 20 #define strange namelist #print warnings... '' converted in 'X', '9' converted in 'X9' myNAMELIST<-NAMELIST('pp','oo','ii','','9'); print(myNAMELIST)#NAMELIST with time series... ts1<-TSERIES(1:10,START=c(2000,1),FREQ=12) ts2<-TSERIES(10:20,START=c(2002,5),FREQ=12) myNameList<-NAMELIST(ts1,ts2) print(myNameList) #prints a list with $ts1 and $ts2 elements #please note that names are 'ts1' and 'ts2'... #$ts1 # Jan Feb Mar Apr May Jun Jul Aug Sep Oct #2000 1 2 3 4 5 6 7 8 9 10 #$ts2 # Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec #2002 10 11 12 13 14 15 16 17 #2003 18 19 20 #define strange namelist #print warnings... '' converted in 'X', '9' converted in 'X9' myNAMELIST<-NAMELIST('pp','oo','ii','','9'); print(myNAMELIST)
This function returns a numerical array built with the length of each input argument. Input arguments can be numerical or time series. Input arguments can also be string variables.
NOELS(...)NOELS(...)
... |
List of input arguments. This function accepts input of class |
This function returns an array of class c().
TIMESERIESis.bimetsBIMETS indexingTSDATESLOCSNAMELISTINTSTSINFOTSLOOKTABIT
out_NOELS<-NOELS(c(1,2,3,4),c(5,6,7)) print(out_NOELS) #print c(4,3) out_NOELS<-NOELS(TSERIES(c(1,2,3,4),START=c(2000,1),FREQ=1),c(5,6,7)) print(out_NOELS) #print c(4,3) out_NOELS<-NOELS('aaa','bb') print(out_NOELS) #print c(3,2)out_NOELS<-NOELS(c(1,2,3,4),c(5,6,7)) print(out_NOELS) #print c(4,3) out_NOELS<-NOELS(TSERIES(c(1,2,3,4),START=c(2000,1),FREQ=1),c(5,6,7)) print(out_NOELS) #print c(4,3) out_NOELS<-NOELS('aaa','bb') print(out_NOELS) #print c(3,2)
This function normalizes a numerical array c(YEAR,PERIOD), given a frequency f and PERIOD>=f.
e.g. normalizeYP(c(2000,15),12) = c(2001,3)
normalizeYP(x = NULL, f = NULL)normalizeYP(x = NULL, f = NULL)
x |
Input numerical array |
f |
Frequency of normalization. Must be a positive integer. |
This function returns a numerical array c(YEAR,PERIOD)
#c(2,13) and frequency=4 => c(5,1) print(normalizeYP(c(2,13),4))#c(2,13) and frequency=4 => c(5,1) print(normalizeYP(c(2,13),4))
This function returns the number of time periods that lie between the provided starting period x1=c(YEAR1,PRD1) and the provided ending period x2=c(YEAR2,PRD2), given a frequency f.
NUMPERIOD(x1, x2, f = NULL)NUMPERIOD(x1, x2, f = NULL)
x1 |
Starting period specified as a numerical array |
x2 |
Ending period specified as a numerical array |
f |
Frequency over the year. It must be a positive integer. |
This function returns an integer of class numeric.
normalizeYPfrequencyGETDATELOCSNAMELIST
# f=5, c(3,4) - c(2,3) = 6 periods print(NUMPERIOD(c(2,3),c(3,4),5))# f=5, c(3,4) - c(2,3) = 6 periods print(NUMPERIOD(c(2,3),c(3,4),5))
The OPTIMIZE procedure provides a convenient method for performing optimal control exercises; the procedure maximizes an arbitrary objective-function under the constraints imposed by the econometric model and by user-specified constraints.
An approach to policy evaluation is via a so-called "social welfare function". This approach relaxes the assumptions of the instruments-targets framework, i.e. the RENORM procedure. Rather than assuming specific desired targets for some endogenous variables, it assumes the existence of a social welfare function determining a scalar measure of performance based on both endogenous and policy (exogenous) variables.
The social welfare function can incorporate information about tradeoffs in objectives that are not allowed by the RENORM instruments-targets approach.
BIMETS supplies the OPTIMIZE procedure in order to perform optimal control exercises on econometric models.
The optimization consists of maximizing a social welfare function, i.e. the objective-function, depending on exogenous and (simulated) endogenous variables, subject to user constraints plus the constraints imposed by the econometric model equations. Users are allowed to define constraints and objective-functions of any degree, and are allowed to provide different constraints and objective-functions in different optimization time periods.
The core of the OPTIMIZE procedure is based on a Monte Carlo method that takes advantage of the STOCHSIMULATE procedure. Policy variables, i.e. INSTRUMENT, are uniformly perturbed in the range defined by the user-provided boundaries, then the INSTRUMENT values that i) verify the user-provided constraints and ii) maximize the objective-functions are selected and stored into the optimize element of the output BIMETS model.
The following steps can describe the procedure implemented in OPTIMIZE:
1) check the correctness of input arguments;
2) perform a STOCHSIMULATE by uniformly perturbing the INSTRUMENT variables inside the user-boundaries provided in the OptimizeBounds function argument;
3) during the STOCHSIMULATE, for each period in the optimization TSRANGE: i) discard the stochastic realizations that do not verify the restrictions provided in the OptimizeRestrictions argument; ii) for all the remaining realizations, compute the current value of the objective-functions time series, as defined in the OptimizeFunctions argument, by using the exogenous and (simulated) endogenous stochastic time series;
4) once the STOCHSIMULATE completes, select the stochastic realization that presents the higher value in the sum of the corresponding objective-function time series values, and return, among other data, the related optimal INSTRUMENT time series.
In the following figure, the scatter plot is populated with 2916 objective function stochastic realizations, computed by using the example code at the end of this section; the 210.58 local maximum is highlighted
(i.e. advancedKleinModel$optimize$optFunMax in first example).
In this example:
i) The objective function definition is:
given as the simulated Gross National Product, as the simulated Consumption and as the exogenous Government Expenditure: the basic idea is to maximize Consumption, and secondarily the Gross National Product, while reducing the Government Expenditure;
ii) The INSTRUMENT variables are the Consumption "booster" (i.e. the add-factor, not to be confused with the simulated Consumption in the objective function) and the Government Expenditure, defined over the following domains: , ;
iii) The following restrictions are applied to the INSTRUMENT: , given as the Consumption "booster" (i.e. the add-factor) and as the Government Expenditure;
The figure clearly shows that non-linear restrictions have been applied, and that non-computable objective functions have been discarded, e.g. the stochastic realizations having due to the square root operation in the objective function, given instrument .
OPTIMIZE( model=NULL, simAlgo='GAUSS-SEIDEL', TSRANGE=NULL, simType='DYNAMIC', simConvergence=0.01, simIterLimit=100, ZeroErrorAC=FALSE, BackFill=0, Exogenize=NULL, ConstantAdjustment=NULL, verbose=FALSE, verboseSincePeriod=0, verboseVars=NULL, StochReplica=100, StochSeed=NULL, OptimizeBounds=NULL, OptimizeRestrictions=NULL, OptimizeFunctions=NULL, quietly=FALSE, RESCHECKeqList=NULL, JACOBIAN_SHOCK=1e-4, JacobianDrop=NULL, forceForwardLooking=FALSE, avoidCompliance=FALSE, ...)OPTIMIZE( model=NULL, simAlgo='GAUSS-SEIDEL', TSRANGE=NULL, simType='DYNAMIC', simConvergence=0.01, simIterLimit=100, ZeroErrorAC=FALSE, BackFill=0, Exogenize=NULL, ConstantAdjustment=NULL, verbose=FALSE, verboseSincePeriod=0, verboseVars=NULL, StochReplica=100, StochSeed=NULL, OptimizeBounds=NULL, OptimizeRestrictions=NULL, OptimizeFunctions=NULL, quietly=FALSE, RESCHECKeqList=NULL, JACOBIAN_SHOCK=1e-4, JacobianDrop=NULL, forceForwardLooking=FALSE, avoidCompliance=FALSE, ...)
model |
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simAlgo |
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TSRANGE |
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simType |
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simConvergence |
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simIterLimit |
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ZeroErrorAC |
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BackFill |
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Exogenize |
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ConstantAdjustment |
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verbose |
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verboseSincePeriod |
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verboseVars |
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StochReplica |
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StochSeed |
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OptimizeBounds |
the named |
OptimizeRestrictions |
the named |
OptimizeFunctions |
the named |
quietly |
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RESCHECKeqList |
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JACOBIAN_SHOCK |
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JacobianDrop |
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forceForwardLooking |
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avoidCompliance |
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... |
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This function will add, into the output BIMETS model object, three new named elements, respectively optimize, simulation_MM and INSTRUMENT_MM.
The optimize element is a named list() that contains the following elements:
- INSTRUMENT: a named list that contains the time series of the instrument exogenous variables that verify the OptimizeRestrictions and that allow the objective OptimizeFunctions to be maximized. This element is populated only if a finite solution exists. List names are equal to the names of the related exogenous variables. Users can also declare an endogenous variable as INSTRUMENT variable, by using the OptimizeBounds argument: in this case the constant adjustment (see STOCHSIMULATE) related to the provided endogenous variable will be used as instrument exogenous variable, and this output INSTRUMENT list will contains the constant adjustment time series that allow the objective OptimizeFunction to be maximized (see example);
- optFunMax: the scalar value (local maximum) obtained by evaluating the OptimizeFunctions while the model is fed by the optimized INSTRUMENT time series. This element is populated only if a finite solution exists;
- optFunTS: the time series obtained by evaluating the OptimizeFunctions during each period in the OPTIMIZE TSRANGE while the model is fed by the optimized INSTRUMENT time series. Thus, optFunMax==sum(optFunTS). This element is populated only if a finite solution exists;
- optFunAve: the scalar value that is the mean of all the stochastic OptimizeFunctions realizations, filtered by the restrictions imposed by the OptimizeRestrictions argument. This element is populated only if a finite solution exists;
- optFunSd: the scalar value that is the standard deviation of all the stochastic OptimizeFunctions realizations, filtered by the restrictions imposed by the OptimizeRestrictions argument. This element is populated only if a finite solution exists;
- realizationsToKeep: a 1 x StochReplica boolean row array. If the i-th element is TRUE than the related objective function realization is computable and verifies the restrictions imposed by the OptimizeRestricions argument. It can be useful along with optFunResults and INSTRUMENT_MM in order to verify and to refine results;
- optFunResults: the numerical array containing the evaluated OptimizeFunctions for all the (unfiltered) realizations;
- modelData: the whole model input dataset wherein the INSTRUMENT exogenous variables have been modified accordingly to the OPTIMIZE results. This data can be useful in order to verify or to refine results (see example);
- ConstantAdjustment: a modified constant adjustment input list wherein the constant adjustment time series related to a INSTRUMENT endogenous variables have been modified accordingly to the OPTIMIZE results. This data can be useful in order to verify or to refine results (see example);
The arguments passed to the function call during the latest OPTIMIZE run will be inserted into the '__OPT_PARAMETERS__' element of the model optimize list; this data can be helpful in order to replicate the optimization results.
The simulation_MM element is a named list(), having the endogenous variables as names. Each element will contain an R x C matrix, given R the number of observations in the optimization TSRANGE and C=1+StochReplica. The first column of each matrix contains the related endogenous variable's unperturbed simulated values; the remaining columns will contain all the StochReplica stochastic realizations for the related endogenous variable.
The INSTRUMENT_MM element is a named list(), having INSTRUMENT variables as names. Each element will contain an R x C matrix, given R the number of observations in the optimization TSRANGE and C=1+StochReplica. The first column of each matrix contains the related INSTRUMENT variable's unperturbed values; the remaining columns will contain all the StochReplica stochastic realizations for the related INSTRUMENT variable.
MDLLOAD_MODELESTIMATESTOCHSIMULATEMULTMATRIXRENORMTIMESERIESBIMETS indexingBIMETS configuration
#define the advanced Klein model advancedKleinModelDef <- " MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional equation evaluations COMMENT> Consumption with autocorrelation on errors BEHAVIORAL> cn TSRANGE 1923 1 1940 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment with restrictions BEHAVIORAL> i TSRANGE 1923 1 1940 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor with PDL BEHAVIORAL> w1 TSRANGE 1923 1 1940 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 2 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with IF switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END " #load the model advancedKleinModel <- LOAD_MODEL(modelText = advancedKleinModelDef) #define data kleinModelData <- list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8, 55,50.9,45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7, 10.2,9.3,10,10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2, -5.1,-3,-1.3,2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6, 210.6,215.7,216.7,213.3,207.1,202,199,197.7,199.8, 201.8,199.9,201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7, 15.6,11.4,7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3, 37.9,34.5,29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7, 50.7,41.3,45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4, 6.8,7.2,8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time=TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0, 1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8, 5.3,5.6,6,6.1,7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load time series into the model object advancedKleinModel <- LOAD_MODEL_DATA(advancedKleinModel,kleinModelData) #estimate the model advancedKleinModel <- ESTIMATE(advancedKleinModel, quietly=TRUE) #we want to maximize the non-linear objective function: #f()=(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5 #in 1942 by using INSTRUMENT cn in range (-5,5) #(cn is endogenous so we use the add-factor) #and g in range (15,25) #we will also impose the following non-linear restriction: #g+(cn^2)/2<27 & g+cn>17 #we need to extend exogenous variables up to 1942 advancedKleinModel$modelData <- within(advancedKleinModel$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1942,1),EXTMODE='CONSTANT') t = TSEXTEND(t, UPTO=c(1942,1),EXTMODE='LINEAR') g = TSEXTEND(g, UPTO=c(1942,1),EXTMODE='CONSTANT') k = TSEXTEND(k, UPTO=c(1942,1),EXTMODE='LINEAR') time = TSEXTEND(time,UPTO=c(1942,1),EXTMODE='LINEAR') }) #define INSTRUMENT and boundaries myOptimizeBounds <- list( cn=list(TSRANGE=TRUE, BOUNDS=c(-5,5)), g=list(TSRANGE=TRUE, BOUNDS=c(15,25)) ) #define restrictions myOptimizeRestrictions <- list( myRes1=list( TSRANGE=TRUE, INEQUALITY='g+(cn^2)/2<27 & g+cn>17') ) #define objective function myOptimizeFunctions <- list( myFun1=list( TSRANGE=TRUE, FUNCTION='(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5') ) #Monte-Carlo optimization by using 10000 stochastic realizations #and 1E-4 convergence criterion advancedKleinModel <- OPTIMIZE(advancedKleinModel ,simType = 'FORECAST' ,TSRANGE=c(1942,1,1942,1) ,simConvergence= 1E-4 ,simIterLimit = 1000 ,StochReplica = 10000 ,StochSeed = 123 ,OptimizeBounds = myOptimizeBounds ,OptimizeRestrictions = myOptimizeRestrictions ,OptimizeFunctions = myOptimizeFunctions) #OPTIMIZE(): optimization boundaries for the add-factor of endogenous # variable "cn" are (-5,5) from year-period 1942-1 to 1942-1. #OPTIMIZE(): optimization boundaries for the exogenous # variable "g" are (15,25) from year-period 1942-1 to 1942-1. #OPTIMIZE(): optimization restriction "myRes1" is active # from year-period 1942-1 to 1942-1. #OPTIMIZE(): optimization objective function "myFun1" is active # from year-period 1942-1 to 1942-1. # #Optimize: 100.00 % #OPTIMIZE(): 2916 out of 10000 objective function realizations (29%) # are finite and verify the provided restrictions. #...OPTIMIZE OK #print local maximum advancedKleinModel$optimize$optFunMax #[1] 210.5755 #print INSTRUMENT that allow local maximum to be achieved advancedKleinModel$optimize$INSTRUMENT #$cn #Time Series: #Start = 1942 #End = 1942 #Frequency = 1 #[1] 2.032203 # #$g #Time Series: #Start = 1942 #End = 1942 #Frequency = 1 #[1] 24.89773 #LET'S VERIFY RESULTS #copy into modelData the computed INSTRUMENT #that allow to maximize the objective function advancedKleinModel$modelData <- advancedKleinModel$optimize$modelData #simulate the model by using the new INSTRUMENT #note: we used cn add-factor as OPTIMIZE instrument, so we need #to pass the computed cn add-factor to the SIMULATE call newConstantAdjustment <- advancedKleinModel$optimize$ConstantAdjustment advancedKleinModel <- SIMULATE(advancedKleinModel ,simType = 'FORECAST' ,TSRANGE = c(1942,1,1942,1) ,simConvergence = 1E-5 ,simIterLimit = 1000 ,ConstantAdjustment = newConstantAdjustment ) #calculate objective function by using the SIMULATE output time series #(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5 y <- advancedKleinModel$simulation$y cn <- advancedKleinModel$simulation$cn g <- advancedKleinModel$modelData$g optFunTest <- (y-110)+(cn-90)*abs(cn-90)-(g-20)^0.5 #verify computed max is equal to optimization max #(in the following command TSPROJECT could be omitted because #myFun1$TSRANGE = TRUE) abs(sum(TSPROJECT(optFunTest ,TSRANGE=c(1942,1,1942,1) ,ARRAY = TRUE) ) - advancedKleinModel$optimize$optFunMax) < 1E-4 #[1] TRUE #we can also check that the SIMULATE time series #are equal to the OPTIMIZE realizations that allow to maximize #the objective function #get realization index that maximizes the objective function maximizingRealizationIdx <- with(advancedKleinModel$optimize, which.max(optFunResults[realizationsToKeep])) #get stochastic realizations unfiltered #(simulation_MM and INSTRUMENT_MM are populated during the OPTIMIZE call) y_opt <- advancedKleinModel$simulation_MM$y cn_opt <- advancedKleinModel$simulation_MM$cn g_opt <- advancedKleinModel$INSTRUMENT_MM$g #filter by restrictions and by finite solutions #(first column in all matrices is related to the un-perturbed model) y_opt <- y_opt[ ,c(FALSE,advancedKleinModel$optimize$realizationsToKeep),drop=FALSE] cn_opt <- cn_opt[,c(FALSE,advancedKleinModel$optimize$realizationsToKeep),drop=FALSE] g_opt <- g_opt[ ,c(FALSE,advancedKleinModel$optimize$realizationsToKeep),drop=FALSE] #get maximizing realizations y_opt <- y_opt[ ,maximizingRealizationIdx,drop=FALSE] cn_opt <- cn_opt[,maximizingRealizationIdx,drop=FALSE] g_opt <- g_opt[ ,maximizingRealizationIdx,drop=FALSE] #verify that these variables are equal to the SIMULATE time series max(abs(y-y_opt)) < 1E-4 #[1] TRUE max(abs(cn-cn_opt)) < 1E-4 #[1] TRUE max(abs(g[[1942,1]]-g_opt)) < 1E-4 #[1] TRUE ############################################################ #MULTI RESTRICTIONS, MULTI OBJECTIVE FUNCTIONS EXAMPLE #load the model (reset stuff) advancedKleinModel <- LOAD_MODEL(modelText = advancedKleinModelDef) #load time series into the model object advancedKleinModel <- LOAD_MODEL_DATA(advancedKleinModel,kleinModelData) #estimate the model advancedKleinModel <- ESTIMATE(advancedKleinModel, quietly=TRUE) #we want to maximize the non-linear objective function: #f1()=(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5 #in 1942 by using INSTRUMENT cn in range (-5,5) #(cn is endogenous so we use the add-factor) #and g in range (15,25) #we want to maximize the non-linear objective function: #f2()=(y-120)+(cn-100)*ABS(cn-100)-(g-20)^0.5-(w2-8)^0.5 #in 1943 by using INSTRUMENT cn in range (-5,5), #g in range (15,25) #and w2 in range (7.5,12.5) #we will also impose the following non-linear restrictions: #in 1942: g+(cn^2)/2<27 & g+cn>17 #in 1943: (g^2)/10+(cn^2)/2+w2^2 < 200 #we need to extend exogenous variables up to 1943 advancedKleinModel$modelData <- within(advancedKleinModel$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1943,1),EXTMODE='CONSTANT') t = TSEXTEND(t, UPTO=c(1943,1),EXTMODE='LINEAR') g = TSEXTEND(g, UPTO=c(1943,1),EXTMODE='CONSTANT') k = TSEXTEND(k, UPTO=c(1943,1),EXTMODE='LINEAR') time = TSEXTEND(time,UPTO=c(1943,1),EXTMODE='LINEAR') }) #define INSTRUMENT and boundaries myOptimizeBounds <- list( cn=list(TSRANGE=TRUE, BOUNDS=c(-5,5)), g=list(TSRANGE=TRUE, BOUNDS=c(15,25)), w2=list(TSRANGE=c(1943,1,1943,1), BOUNDS=c(7.5,12.5)) ) #define restrictions myOptimizeRestrictions <- list( myRes1=list( TSRANGE=c(1942,1,1942,1), INEQUALITY='g+(cn^2)/2 < 27 & g+cn > 17'), myRes2=list( TSRANGE=c(1943,1,1943,1), INEQUALITY='(g^2)/10+(cn^2)/2+w2^2 < 200') ) #define objective functions myOptimizeFunctions <- list( myFun1=list( TSRANGE=c(1942,1,1942,1), FUNCTION='(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5'), myFun2=list( TSRANGE=c(1943,1,1943,1), FUNCTION='(y-120)+(cn-100)*ABS(cn-100)-(g-20)^0.5-(w2-8)^0.5') ) #Monte-Carlo optimization by using 1000 stochastic realizations #and 1E-4 convergence advancedKleinModel <- OPTIMIZE(advancedKleinModel ,simType = 'FORECAST' ,TSRANGE=c(1942,1,1943,1) ,simConvergence=1E-4 ,simIterLimit = 500 ,StochReplica = 1000 ,StochSeed = 123 ,OptimizeBounds = myOptimizeBounds ,OptimizeRestrictions = myOptimizeRestrictions ,OptimizeFunctions = myOptimizeFunctions) #print INSTRUMENT that allow local maximum to be achieved advancedKleinModel$optimize$INSTRUMENT #LET'S VERIFY RESULTS #copy into modelData the computed INSTRUMENT #that allow to maximize the objective function advancedKleinModel$modelData <- advancedKleinModel$optimize$modelData #simulate the model by using the new INSTRUMENT newConstantAdjustment <- advancedKleinModel$optimize$ConstantAdjustment advancedKleinModel <- SIMULATE(advancedKleinModel ,simType = 'FORECAST' ,TSRANGE = c(1942,1,1943,1) ,simConvergence = 1E-5 ,simIterLimit = 100 ,ConstantAdjustment = newConstantAdjustment ) #calculate objective functions by using the SIMULATE output time series y <- advancedKleinModel$simulation$y cn <- advancedKleinModel$simulation$cn g <- advancedKleinModel$modelData$g w2 <- advancedKleinModel$modelData$w2 optFunTest1 <- (y-110)+(cn-90)*abs(cn-90)-(g-20)^0.5 optFunTest2 <- (y-120)+(cn-100)*abs(cn-100)-(g-20)^0.5-(w2-8)^0.5 #verify computed max is equal to optimization max abs(sum(TSPROJECT(optFunTest1 ,TSRANGE=c(1942,1,1942,1) ,ARRAY = TRUE)+ TSPROJECT(optFunTest2 ,TSRANGE=c(1943,1,1943,1) ,ARRAY = TRUE) ) - advancedKleinModel$optimize$optFunMax) < 1E-2 #[1] TRUE#define the advanced Klein model advancedKleinModelDef <- " MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional equation evaluations COMMENT> Consumption with autocorrelation on errors BEHAVIORAL> cn TSRANGE 1923 1 1940 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment with restrictions BEHAVIORAL> i TSRANGE 1923 1 1940 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor with PDL BEHAVIORAL> w1 TSRANGE 1923 1 1940 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 2 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with IF switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END " #load the model advancedKleinModel <- LOAD_MODEL(modelText = advancedKleinModelDef) #define data kleinModelData <- list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8, 55,50.9,45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7, 10.2,9.3,10,10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2, -5.1,-3,-1.3,2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6, 210.6,215.7,216.7,213.3,207.1,202,199,197.7,199.8, 201.8,199.9,201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7, 15.6,11.4,7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3, 37.9,34.5,29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7, 50.7,41.3,45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4, 6.8,7.2,8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time=TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0, 1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8, 5.3,5.6,6,6.1,7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load time series into the model object advancedKleinModel <- LOAD_MODEL_DATA(advancedKleinModel,kleinModelData) #estimate the model advancedKleinModel <- ESTIMATE(advancedKleinModel, quietly=TRUE) #we want to maximize the non-linear objective function: #f()=(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5 #in 1942 by using INSTRUMENT cn in range (-5,5) #(cn is endogenous so we use the add-factor) #and g in range (15,25) #we will also impose the following non-linear restriction: #g+(cn^2)/2<27 & g+cn>17 #we need to extend exogenous variables up to 1942 advancedKleinModel$modelData <- within(advancedKleinModel$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1942,1),EXTMODE='CONSTANT') t = TSEXTEND(t, UPTO=c(1942,1),EXTMODE='LINEAR') g = TSEXTEND(g, UPTO=c(1942,1),EXTMODE='CONSTANT') k = TSEXTEND(k, UPTO=c(1942,1),EXTMODE='LINEAR') time = TSEXTEND(time,UPTO=c(1942,1),EXTMODE='LINEAR') }) #define INSTRUMENT and boundaries myOptimizeBounds <- list( cn=list(TSRANGE=TRUE, BOUNDS=c(-5,5)), g=list(TSRANGE=TRUE, BOUNDS=c(15,25)) ) #define restrictions myOptimizeRestrictions <- list( myRes1=list( TSRANGE=TRUE, INEQUALITY='g+(cn^2)/2<27 & g+cn>17') ) #define objective function myOptimizeFunctions <- list( myFun1=list( TSRANGE=TRUE, FUNCTION='(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5') ) #Monte-Carlo optimization by using 10000 stochastic realizations #and 1E-4 convergence criterion advancedKleinModel <- OPTIMIZE(advancedKleinModel ,simType = 'FORECAST' ,TSRANGE=c(1942,1,1942,1) ,simConvergence= 1E-4 ,simIterLimit = 1000 ,StochReplica = 10000 ,StochSeed = 123 ,OptimizeBounds = myOptimizeBounds ,OptimizeRestrictions = myOptimizeRestrictions ,OptimizeFunctions = myOptimizeFunctions) #OPTIMIZE(): optimization boundaries for the add-factor of endogenous # variable "cn" are (-5,5) from year-period 1942-1 to 1942-1. #OPTIMIZE(): optimization boundaries for the exogenous # variable "g" are (15,25) from year-period 1942-1 to 1942-1. #OPTIMIZE(): optimization restriction "myRes1" is active # from year-period 1942-1 to 1942-1. #OPTIMIZE(): optimization objective function "myFun1" is active # from year-period 1942-1 to 1942-1. # #Optimize: 100.00 % #OPTIMIZE(): 2916 out of 10000 objective function realizations (29%) # are finite and verify the provided restrictions. #...OPTIMIZE OK #print local maximum advancedKleinModel$optimize$optFunMax #[1] 210.5755 #print INSTRUMENT that allow local maximum to be achieved advancedKleinModel$optimize$INSTRUMENT #$cn #Time Series: #Start = 1942 #End = 1942 #Frequency = 1 #[1] 2.032203 # #$g #Time Series: #Start = 1942 #End = 1942 #Frequency = 1 #[1] 24.89773 #LET'S VERIFY RESULTS #copy into modelData the computed INSTRUMENT #that allow to maximize the objective function advancedKleinModel$modelData <- advancedKleinModel$optimize$modelData #simulate the model by using the new INSTRUMENT #note: we used cn add-factor as OPTIMIZE instrument, so we need #to pass the computed cn add-factor to the SIMULATE call newConstantAdjustment <- advancedKleinModel$optimize$ConstantAdjustment advancedKleinModel <- SIMULATE(advancedKleinModel ,simType = 'FORECAST' ,TSRANGE = c(1942,1,1942,1) ,simConvergence = 1E-5 ,simIterLimit = 1000 ,ConstantAdjustment = newConstantAdjustment ) #calculate objective function by using the SIMULATE output time series #(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5 y <- advancedKleinModel$simulation$y cn <- advancedKleinModel$simulation$cn g <- advancedKleinModel$modelData$g optFunTest <- (y-110)+(cn-90)*abs(cn-90)-(g-20)^0.5 #verify computed max is equal to optimization max #(in the following command TSPROJECT could be omitted because #myFun1$TSRANGE = TRUE) abs(sum(TSPROJECT(optFunTest ,TSRANGE=c(1942,1,1942,1) ,ARRAY = TRUE) ) - advancedKleinModel$optimize$optFunMax) < 1E-4 #[1] TRUE #we can also check that the SIMULATE time series #are equal to the OPTIMIZE realizations that allow to maximize #the objective function #get realization index that maximizes the objective function maximizingRealizationIdx <- with(advancedKleinModel$optimize, which.max(optFunResults[realizationsToKeep])) #get stochastic realizations unfiltered #(simulation_MM and INSTRUMENT_MM are populated during the OPTIMIZE call) y_opt <- advancedKleinModel$simulation_MM$y cn_opt <- advancedKleinModel$simulation_MM$cn g_opt <- advancedKleinModel$INSTRUMENT_MM$g #filter by restrictions and by finite solutions #(first column in all matrices is related to the un-perturbed model) y_opt <- y_opt[ ,c(FALSE,advancedKleinModel$optimize$realizationsToKeep),drop=FALSE] cn_opt <- cn_opt[,c(FALSE,advancedKleinModel$optimize$realizationsToKeep),drop=FALSE] g_opt <- g_opt[ ,c(FALSE,advancedKleinModel$optimize$realizationsToKeep),drop=FALSE] #get maximizing realizations y_opt <- y_opt[ ,maximizingRealizationIdx,drop=FALSE] cn_opt <- cn_opt[,maximizingRealizationIdx,drop=FALSE] g_opt <- g_opt[ ,maximizingRealizationIdx,drop=FALSE] #verify that these variables are equal to the SIMULATE time series max(abs(y-y_opt)) < 1E-4 #[1] TRUE max(abs(cn-cn_opt)) < 1E-4 #[1] TRUE max(abs(g[[1942,1]]-g_opt)) < 1E-4 #[1] TRUE ############################################################ #MULTI RESTRICTIONS, MULTI OBJECTIVE FUNCTIONS EXAMPLE #load the model (reset stuff) advancedKleinModel <- LOAD_MODEL(modelText = advancedKleinModelDef) #load time series into the model object advancedKleinModel <- LOAD_MODEL_DATA(advancedKleinModel,kleinModelData) #estimate the model advancedKleinModel <- ESTIMATE(advancedKleinModel, quietly=TRUE) #we want to maximize the non-linear objective function: #f1()=(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5 #in 1942 by using INSTRUMENT cn in range (-5,5) #(cn is endogenous so we use the add-factor) #and g in range (15,25) #we want to maximize the non-linear objective function: #f2()=(y-120)+(cn-100)*ABS(cn-100)-(g-20)^0.5-(w2-8)^0.5 #in 1943 by using INSTRUMENT cn in range (-5,5), #g in range (15,25) #and w2 in range (7.5,12.5) #we will also impose the following non-linear restrictions: #in 1942: g+(cn^2)/2<27 & g+cn>17 #in 1943: (g^2)/10+(cn^2)/2+w2^2 < 200 #we need to extend exogenous variables up to 1943 advancedKleinModel$modelData <- within(advancedKleinModel$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1943,1),EXTMODE='CONSTANT') t = TSEXTEND(t, UPTO=c(1943,1),EXTMODE='LINEAR') g = TSEXTEND(g, UPTO=c(1943,1),EXTMODE='CONSTANT') k = TSEXTEND(k, UPTO=c(1943,1),EXTMODE='LINEAR') time = TSEXTEND(time,UPTO=c(1943,1),EXTMODE='LINEAR') }) #define INSTRUMENT and boundaries myOptimizeBounds <- list( cn=list(TSRANGE=TRUE, BOUNDS=c(-5,5)), g=list(TSRANGE=TRUE, BOUNDS=c(15,25)), w2=list(TSRANGE=c(1943,1,1943,1), BOUNDS=c(7.5,12.5)) ) #define restrictions myOptimizeRestrictions <- list( myRes1=list( TSRANGE=c(1942,1,1942,1), INEQUALITY='g+(cn^2)/2 < 27 & g+cn > 17'), myRes2=list( TSRANGE=c(1943,1,1943,1), INEQUALITY='(g^2)/10+(cn^2)/2+w2^2 < 200') ) #define objective functions myOptimizeFunctions <- list( myFun1=list( TSRANGE=c(1942,1,1942,1), FUNCTION='(y-110)+(cn-90)*ABS(cn-90)-(g-20)^0.5'), myFun2=list( TSRANGE=c(1943,1,1943,1), FUNCTION='(y-120)+(cn-100)*ABS(cn-100)-(g-20)^0.5-(w2-8)^0.5') ) #Monte-Carlo optimization by using 1000 stochastic realizations #and 1E-4 convergence advancedKleinModel <- OPTIMIZE(advancedKleinModel ,simType = 'FORECAST' ,TSRANGE=c(1942,1,1943,1) ,simConvergence=1E-4 ,simIterLimit = 500 ,StochReplica = 1000 ,StochSeed = 123 ,OptimizeBounds = myOptimizeBounds ,OptimizeRestrictions = myOptimizeRestrictions ,OptimizeFunctions = myOptimizeFunctions) #print INSTRUMENT that allow local maximum to be achieved advancedKleinModel$optimize$INSTRUMENT #LET'S VERIFY RESULTS #copy into modelData the computed INSTRUMENT #that allow to maximize the objective function advancedKleinModel$modelData <- advancedKleinModel$optimize$modelData #simulate the model by using the new INSTRUMENT newConstantAdjustment <- advancedKleinModel$optimize$ConstantAdjustment advancedKleinModel <- SIMULATE(advancedKleinModel ,simType = 'FORECAST' ,TSRANGE = c(1942,1,1943,1) ,simConvergence = 1E-5 ,simIterLimit = 100 ,ConstantAdjustment = newConstantAdjustment ) #calculate objective functions by using the SIMULATE output time series y <- advancedKleinModel$simulation$y cn <- advancedKleinModel$simulation$cn g <- advancedKleinModel$modelData$g w2 <- advancedKleinModel$modelData$w2 optFunTest1 <- (y-110)+(cn-90)*abs(cn-90)-(g-20)^0.5 optFunTest2 <- (y-120)+(cn-100)*abs(cn-100)-(g-20)^0.5-(w2-8)^0.5 #verify computed max is equal to optimization max abs(sum(TSPROJECT(optFunTest1 ,TSRANGE=c(1942,1,1942,1) ,ARRAY = TRUE)+ TSPROJECT(optFunTest2 ,TSRANGE=c(1943,1,1943,1) ,ARRAY = TRUE) ) - advancedKleinModel$optimize$optFunMax) < 1E-2 #[1] TRUE
This function returns a quarterly (dis)aggregated time series, using as input an annual, semiannual, monthly or daily time series.
QUARTERLY(x = NULL, fun = NULL, avoidCompliance = FALSE, ...)QUARTERLY(x = NULL, fun = NULL, avoidCompliance = FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
fun |
Only for daily or monthly input time series: |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a quarterly BIMETS time series.
#TS YEARLY TO QUARTERLY n<-10 ts1<-TSERIES(1:n,START=c(2000,1),FREQ=1) ts1[5]<-NA TABIT(QUARTERLY(ts1,fun='INTERP_CENTER')); #TS DAILY TO QUARTERLY n<-600 ts1<-TSERIES(1:n,START=c(2000,1),FREQ='D') ts1[25]<-NA TABIT(QUARTERLY(ts1,fun='SUM'))#TS YEARLY TO QUARTERLY n<-10 ts1<-TSERIES(1:n,START=c(2000,1),FREQ=1) ts1[5]<-NA TABIT(QUARTERLY(ts1,fun='INTERP_CENTER')); #TS DAILY TO QUARTERLY n<-600 ts1<-TSERIES(1:n,START=c(2000,1),FREQ='D') ts1[25]<-NA TABIT(QUARTERLY(ts1,fun='SUM'))
The endogenous targeting of econometric models (a.k.a. "renormalization") consists of solving the model while interchanging the role of one or more endogenous variables with an equal number of exogenous variables.
This procedure determines the values for the INSTRUMENT exogenous variables that allow the objective TARGET endogenous values to be achieved, with respect to the constraints given by the model equations (see MDL).
This is an approach to economic and monetary policy analysis, and is based on two assumptions:
1. there exists a desired level for a set of the n endogenous variables defined as TARGET;
2. there exists a set of the n exogenous variables defined as INSTRUMENT;
Given these premises, the endogenous targeting process consists in determining the values of the exogenous variables chosen as INSTRUMENT allowing us to achieve the desired values for the endogenous variables designated as TARGET. In other words the procedure allows users to exchange the role of exogenous and endogenous among a set of variables pairs.
Given a list of exogenous INSTRUMENT variables and a list of TARGET endogenous time series, the iterative procedure can be split into the following steps:
1. Computation of the multipliers matrix MULTMAT of the TARGET endogenous variables with respect to the INSTRUMENT exogenous variables (this is a square matrix by construction);
2. Solution of the linear system (if any): MULTMAT TARGET , where are the exogenous variables in the INSTRUMENT list and are the endogenous variables that have a related target in the TARGET list, given the current iteration;
3. Simulation of the model with the new set of exogenous variables computed in step 2, then a convergence check by comparing the subset of endogenous variables arising from this simulation and the related time series in TARGET list. If the convergence condition is satisfied, or the maximum number of iterations is reached, the algorithm will stop, otherwise it will go back to step 1;
Users can also declare an endogenous variable as an INSTRUMENT variable. In this case, the constant adjustment (see SIMULATE) related to the provided endogenous variable will be used as the instrument exogenous variable. This procedure is particularly suited for the automatic computation of the add-factors needed to fine tune the model into a baseline path and to improve the forecasting accuracy.
If the convergence condition is satisfied, the RENORM procedure will return the INSTRUMENT time series allowing us to achieve the desired values for the endogenous variables designated as TARGET.
For more realistic scenarios, several advanced econometric exercises on the US Federal Reserve FRB/US econometric model (e.g., dynamic simulation in a monetary policy shock, rational expectations, endogenous targeting, stochastic simulation, etc.) are available in the "US Federal Reserve quarterly model (FRB/US) in R with bimets" vignette.
RENORM(model=NULL, simAlgo='GAUSS-SEIDEL', TSRANGE=NULL, simType='DYNAMIC', simConvergence=0.01, simIterLimit=100, ZeroErrorAC=FALSE, BackFill=0, Exogenize=NULL, ConstantAdjustment=NULL, verbose=FALSE, verboseSincePeriod=0, verboseVars=NULL, renormIterLimit=10, renormConvergence=1e-4, TARGET=NULL, INSTRUMENT=NULL, MM_SHOCK=0.00001, quietly=FALSE, quietlyMULTMATRIX=FALSE, tol=1e-28, JACOBIAN_SHOCK=1e-4, JacobianDrop=NULL, forceForwardLooking=FALSE, avoidCompliance=FALSE, ... )RENORM(model=NULL, simAlgo='GAUSS-SEIDEL', TSRANGE=NULL, simType='DYNAMIC', simConvergence=0.01, simIterLimit=100, ZeroErrorAC=FALSE, BackFill=0, Exogenize=NULL, ConstantAdjustment=NULL, verbose=FALSE, verboseSincePeriod=0, verboseVars=NULL, renormIterLimit=10, renormConvergence=1e-4, TARGET=NULL, INSTRUMENT=NULL, MM_SHOCK=0.00001, quietly=FALSE, quietlyMULTMATRIX=FALSE, tol=1e-28, JACOBIAN_SHOCK=1e-4, JacobianDrop=NULL, forceForwardLooking=FALSE, avoidCompliance=FALSE, ... )
model |
see |
simAlgo |
see |
TSRANGE |
see |
simType |
see |
simConvergence |
see |
simIterLimit |
see |
ZeroErrorAC |
see |
BackFill |
see |
Exogenize |
see |
ConstantAdjustment |
see |
verbose |
see |
verboseSincePeriod |
see |
verboseVars |
see |
renormIterLimit |
The value representing the maximum number of iterations to be performed. The iterative renormalization procedure will stop when |
renormConvergence |
The convergence value requested for the iterative renormalization process, that stops when the Euclidean distance between each |
TARGET |
A named list that specifies the target endogenous variables. List names must be equal to the names of the target endogenous variables involved in the renormalization; each list element must contain the time series of the desired target endogenous values; time series must be compliant with the compliance control check defined in |
INSTRUMENT |
A |
tol |
the tolerance for detecting linear dependencies in the columns of a matrix while an inversion is requested. |
MM_SHOCK |
see |
quietly |
If |
quietlyMULTMATRIX |
If |
JACOBIAN_SHOCK |
see |
JacobianDrop |
see |
forceForwardLooking |
see |
avoidCompliance |
see |
... |
see |
This function will add a new named element renorm into the output BIMETS model object.
This new renorm element is a named list that contains the following elements:
- INSTRUMENT: a named list that contains the INSTRUMENT exogenous time series that allow the objective TARGET endogenous values to be achieved. This element is populated only if the convergence is reached. List names are equal to the names of the related exogenous variables. Users can also declare an endogenous variable as INSTRUMENT variable: in this case the constant adjustment (see SIMULATE) related to the provided endogenous variable will be used as instrument exogenous variable, and this INSTRUMENT output list will contains the constant adjustment time series that allow the objective TARGET endogenous values to be achieved (see example);
- TARGET: a named list built with the achieved TARGET endogenous time series. List names are equal to the target endogenous variable names;
- unConvergedTARGET: the names array of the endogenous TARGET variables that failed the convergence. This element is populated only if the convergence has not been reached;
- modelData: the whole model input dataset wherein the INSTRUMENT exogenous variables have been modified accordingly to the RENORM results. This data can be useful in order to refine results or to verify that the model, fed with the proper INSTRUMENT exogenous time series, produces the desired TARGET endogenous values. This element is populated only if the convergence is achieved (see example);
- ConstantAdjustment: a modified constant adjustment input list (see SIMULATE) wherein the constant adjustment time series related to a INSTRUMENT endogenous variables have been modified accordingly to the RENORM results. This data can be useful in order to refine results or to verify that the model, fed with the proper INSTRUMENT exogenous time series (therefore with the proper ConstantAdjustment time series, if any), produces the desired TARGET endogenous values (see example). This element is populated only if the convergence is achieved;
- __RENORM_PARAMETERS__: a named list that contains the arguments passed to the function call during the latest RENORM run, e.g. TSRANGE, INSTRUMENT, TARGET, renormIterLimit, renormConvergence, ConstantAdjustment, Exogenize, etc.: this data can be useful in order to replicate renorm results.
MDLLOAD_MODELESTIMATESIMULATESTOCHSIMULATEMULTMATRIXOPTIMIZETIMESERIESBIMETS indexingBIMETS configuration
#define model myModelDefinition<- "MODEL COMMENT> Klein Model 1 of the U.S. Economy COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1921 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data myModel<-LOAD_MODEL(modelText=myModelDefinition) myModel<-LOAD_MODEL_DATA(myModel, myModelData) #estimate model myModel<-ESTIMATE(myModel) #we want an arbitrary value of 66 on Consumption 'cn' in 1940 and 78 in 1941 #we want an arbitrary value of 77 on GNP 'y' in 1940 and 98 in 1941 kleinTargets<-list( cn = TSERIES(66,78,START=c(1940,1),FREQ=1), y = TSERIES(77,98,START=c(1940,1),FREQ=1) ) #Then, we can perform the model endogenous targeting by using Government Wage Bill 'w2' #and Government Expenditure 'g' as #INSTRUMENT in the years 1940 and 1941: myModel<-RENORM(myModel ,INSTRUMENT = c('w2','g') ,TARGET = kleinTargets ,TSRANGE = c(1940,1,1941,1) ,simIterLimit = 100 ) with(myModel,TABIT(modelData$w2, renorm$INSTRUMENT$w2, modelData$g, renorm$INSTRUMENT$g)) # Date, Prd., modelData$w2, renorm$INSTRUMENT$w2, modelData$g, renorm$INSTRUMENT$g # etc. # 1938, 1 , 7.7, , 13, # 1939, 1 , 7.8, , 14.4, # 1940, 1 , 8, 7.41333, 15.4, 16.1069 # 1941, 1 , 8.5, 9.3436, 22.3, 22.6599 #So, if we want to achieve on Consumption 'cn' #an arbitrary simulated value of 66 #in 1940 and 78 in 1941, and if we want #to achieve on GNP 'y' an arbitrary #simulated value of 77 in 1940 and 98 in 1941, #we need to change exogenous 'w2' from 8 to 7.41 #in 1940 and from 8.5 to 9.34 in 1941, #and we need to change exogenous 'g' #from 15.4 to 16.1 in 1940 and from 22.3 to 22.66 in 1941 #Let's verify: #create a new model kleinRenorm<-myModel #get instruments to be used newInstruments=myModel$renorm$INSTRUMENT #change exogenous by using new instruments kleinRenorm$modelData<-within(kleinRenorm$modelData, { w2[[1940,1]]=newInstruments$w2[[1940,1]] w2[[1941,1]]=newInstruments$w2[[1941,1]] g[[1940,1]] =newInstruments$g[[1940,1]] g[[1941,1]] =newInstruments$g[[1941,1]] } ) #users can also replace last two commands with: #kleinRenorm$modelData<-kleinRenorm$renorm$modelData #simulate the new model kleinRenorm<-SIMULATE(kleinRenorm ,TSRANGE=c(1940,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ) #Simulation: 100.00% #...SIMULATE OK #verify targets are achieved with(kleinRenorm$simulation, TABIT(cn,y) ) #Date, Prd., cn , y #1940, 1 , 66.01116 , 77.01772 #1941, 1 , 78.02538 , 98.04121 ###################################################################### #now use 'i' endogenous variable as an instrument #first, define the related exogenous constant adjustment myCA<-list(i = myModel$modelData$i*0+0.1) #run renorm with endogenous 'i' as instrument myModel<-RENORM(myModel ,INSTRUMENT = c('w2','i') ,TARGET = kleinTargets ,TSRANGE = c(1940,1,1941,1) ,simIterLimit = 100 ,ConstantAdjustment = myCA ) #get the values of the constant adjustment for the endogenous 'i' #in 1940-1941 that allow achieving the target values for 'cn' and 'y' myModel$renorm$ConstantAdjustment #$i #Time Series: #Start = 1920 #End = 1941 #Frequency = 1 # [1] 0.1000000 0.1000000 0.1000000 ... #[20] 0.1000000 0.7069039 0.4388811 #these values are also reported in the INSTRUMENT output list myModel$renorm$INSTRUMENT$i #Time Series: #Start = 1940 #End = 1941 #Frequency = 1 #[1] 0.7069039 0.4388811#define model myModelDefinition<- "MODEL COMMENT> Klein Model 1 of the U.S. Economy COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1921 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data myModel<-LOAD_MODEL(modelText=myModelDefinition) myModel<-LOAD_MODEL_DATA(myModel, myModelData) #estimate model myModel<-ESTIMATE(myModel) #we want an arbitrary value of 66 on Consumption 'cn' in 1940 and 78 in 1941 #we want an arbitrary value of 77 on GNP 'y' in 1940 and 98 in 1941 kleinTargets<-list( cn = TSERIES(66,78,START=c(1940,1),FREQ=1), y = TSERIES(77,98,START=c(1940,1),FREQ=1) ) #Then, we can perform the model endogenous targeting by using Government Wage Bill 'w2' #and Government Expenditure 'g' as #INSTRUMENT in the years 1940 and 1941: myModel<-RENORM(myModel ,INSTRUMENT = c('w2','g') ,TARGET = kleinTargets ,TSRANGE = c(1940,1,1941,1) ,simIterLimit = 100 ) with(myModel,TABIT(modelData$w2, renorm$INSTRUMENT$w2, modelData$g, renorm$INSTRUMENT$g)) # Date, Prd., modelData$w2, renorm$INSTRUMENT$w2, modelData$g, renorm$INSTRUMENT$g # etc. # 1938, 1 , 7.7, , 13, # 1939, 1 , 7.8, , 14.4, # 1940, 1 , 8, 7.41333, 15.4, 16.1069 # 1941, 1 , 8.5, 9.3436, 22.3, 22.6599 #So, if we want to achieve on Consumption 'cn' #an arbitrary simulated value of 66 #in 1940 and 78 in 1941, and if we want #to achieve on GNP 'y' an arbitrary #simulated value of 77 in 1940 and 98 in 1941, #we need to change exogenous 'w2' from 8 to 7.41 #in 1940 and from 8.5 to 9.34 in 1941, #and we need to change exogenous 'g' #from 15.4 to 16.1 in 1940 and from 22.3 to 22.66 in 1941 #Let's verify: #create a new model kleinRenorm<-myModel #get instruments to be used newInstruments=myModel$renorm$INSTRUMENT #change exogenous by using new instruments kleinRenorm$modelData<-within(kleinRenorm$modelData, { w2[[1940,1]]=newInstruments$w2[[1940,1]] w2[[1941,1]]=newInstruments$w2[[1941,1]] g[[1940,1]] =newInstruments$g[[1940,1]] g[[1941,1]] =newInstruments$g[[1941,1]] } ) #users can also replace last two commands with: #kleinRenorm$modelData<-kleinRenorm$renorm$modelData #simulate the new model kleinRenorm<-SIMULATE(kleinRenorm ,TSRANGE=c(1940,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ) #Simulation: 100.00% #...SIMULATE OK #verify targets are achieved with(kleinRenorm$simulation, TABIT(cn,y) ) #Date, Prd., cn , y #1940, 1 , 66.01116 , 77.01772 #1941, 1 , 78.02538 , 98.04121 ###################################################################### #now use 'i' endogenous variable as an instrument #first, define the related exogenous constant adjustment myCA<-list(i = myModel$modelData$i*0+0.1) #run renorm with endogenous 'i' as instrument myModel<-RENORM(myModel ,INSTRUMENT = c('w2','i') ,TARGET = kleinTargets ,TSRANGE = c(1940,1,1941,1) ,simIterLimit = 100 ,ConstantAdjustment = myCA ) #get the values of the constant adjustment for the endogenous 'i' #in 1940-1941 that allow achieving the target values for 'cn' and 'y' myModel$renorm$ConstantAdjustment #$i #Time Series: #Start = 1920 #End = 1941 #Frequency = 1 # [1] 0.1000000 0.1000000 0.1000000 ... #[20] 0.1000000 0.7069039 0.4388811 #these values are also reported in the INSTRUMENT output list myModel$renorm$INSTRUMENT$i #Time Series: #Start = 1940 #End = 1941 #Frequency = 1 #[1] 0.7069039 0.4388811
This function returns a semi-annual (dis)aggregated time series, by using as input an annual, quarterly, monthly or daily time series.
SEMIANNUAL(x = NULL, fun = NULL, avoidCompliance = FALSE, ...)SEMIANNUAL(x = NULL, fun = NULL, avoidCompliance = FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
fun |
Only for daily or monthly or quarterly input time series: |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a semi-annual BIMETS time series.
#TS QUARTERLY TO SEMIANNUAL n<-14 xArr<-(n:0) ts1<-TSERIES(xArr,START=c(2000,1),FREQ='Q') print(SEMIANNUAL(ts1,fun='NAVE')) #TS ANNUAL TO SEMIANNUAL ts1<-TSERIES((1:10),START=c(2000,1),FREQ=1) print(SEMIANNUAL(ts1,fun='INTERP_END'))#TS QUARTERLY TO SEMIANNUAL n<-14 xArr<-(n:0) ts1<-TSERIES(xArr,START=c(2000,1),FREQ='Q') print(SEMIANNUAL(ts1,fun='NAVE')) #TS ANNUAL TO SEMIANNUAL ts1<-TSERIES((1:10),START=c(2000,1),FREQ=1) print(SEMIANNUAL(ts1,fun='INTERP_END'))
The simulation of an econometric model basically consists in solving the system of the equations describing the model for each time period in the specified time interval. Since the equations may not be linear in the variables, and since the graph derived from the "incidence matrix" may be cyclic, the usual methods based on linear algebra are not applicable. The simulation must be solved by using an iterative algorithm (Users can find the "indicence matrix" definition in the following section "The Optimal Reordering").
BIMETS simulation capabilities support:
- Static simulations: a static multiple equation simulation, in which the historical values for the lagged endogenous variables are used in the solutions of subsequent periods;
- Dynamic simulations: a dynamic simulation, in which the simulated values for the lagged endogenous variables are used in the solutions of subsequent periods;
- Residuals check: a single period, single equation simulation; simulated time series in output are just the computation of the RHS (right-hand-side) of their equation, by using the historical values of the involved time series and by accounting for error autocorrelation and PDLs, if any;
- Forecast simulations: similar to dynamic simulation, but during the initialization of the iterative algorithm the starting values of endogenous variables in a period are set equal to the simulated values of the previous period. This allows the simulation of future endogenous observations, i.e. the forecast;
- Stochastic Simulation: see STOCHSIMULATE;
- Partial or total exogenization of endogenous variables: in the provided time interval (i.e. partial exog.) or in whole simulation time range (i.e. total exog.), the values of the selected endogenous variables can be definitely set equal to their historical values, by excluding their equations from the iterative algorithm of simulation;
- Constant adjustment of endogenous variables (add-factors): adds up a new exogenous time series - the "constant adjustment" - in the equation of the selected endogenous variables.
- Gauss-Seidel and Newton-Raphson simulation algorithms: the Gauss-Seidel algorithm is simple, robust, and works well for many backward-looking macro-econometric models. Equations are evaluated as-is in a proper order until the convergence, if any, is verified on the so called "feedback variables" (Users can find the "feedback variable" definition in the next section "The Optimal Reordering"). It is slower than Newton-Raphson algorithms for a very low convergence criterion, and fails to find a convergence for a small set of econometric models, even when a convergence exists. The Newton-Raphson algorithm allows users to solve a broader set of macro-econometric models than the Gauss-Seidel algorithm. Moreover, it is usually faster than the Gauss-Seidel algorithm (on modern computers, users must simulate an extensive econometric model with a low convergence criterion to appreciate the speedup). This type of algorithm requires the construction and the inversion of the Jacobian matrix for the feedback variables; thus, in some scenarios, numerical issues can arise, and users are required to manually exclude some feedback variables from the Jacobian matrix by using the JacobianDrop argument of the SIMULATE procedure.
In details, the generic model suitable for simulation in BIMETS can be written as:
being: the number of equations in the model; the n-dimensional vector of the endogenous variables; the m-dimensional vector of the exogenous variables; any kind of functional expression able to be written by using the MDL syntax;
As described later on, in BIMETS a modified Gauss-Seidel iterative algorithm, or a Newton-Raphson algorithm, can solve the system of equations. The convergence properties may vary depending on the model specifications. In some conditions, the algorithm may not converge for a specific model or a specific set of data.
A convergence criterion and a maximum number of iterations to be performed are provided by default. Users can change these criteria by using the simConvergence and simIterLimit arguments of the SIMULATE function.
The general conceptual scheme of the simulation process (for each time period) is the following:
1. initialize the solution for the current simulation period;
2. iteratively solve the system of equations;
3. save the solution, if any;
Step 2 means that for each iteration, the operations are:
2.1 update the values of the current endogenous variables;
2.2 verify that the convergence criterion is satisfied or that the maximum number of allowed iterations has been reached;
The initial solution for the iterative process (step 1) can be given alternatively by:
- the historical value of the endogenous variables for the current simulation period (the default);
- the simulated value of the endogenous variables from the previous simulation period (this alternative is driven by the simType='FORECAST' argument of the SIMULATE function);
In the "dynamic" simulations (i.e. simulations performed by using either the default simType='DYNAMIC' or the simType='FORECAST'), whenever lagged endogenous variables are needed in the computation, the simulated values of the endogenous variables assessed in the previous time periods are used. In this case, the simulation results in a given time period depend on the simulation results in the previous time periods. This kind of simulation is defined as "multiple equation, multiple period".
As an alternative, the actual historical values can be used in the "static" simulations (i.e. simulations performed by using simType='STATIC') rather than simulated values whenever lagged endogenous variables are needed in the computations. In this case, the simulation results in a given time period do not depend on the simulation results in the previous time periods. This kind of simulation is defined as "multiple equation, single period".
The last simulation type available is the residual check (simType='RESCHECK'). With this option, a "single equation, single period" simulation is performed. In this case, no iteration must be carried out. The endogenous variables are assessed for each time period by using historical values for each variable on the right-hand side of the equation, for both lagged and current periods. This kind of simulation helps debug and check of the logical coherence of the equations and the data, and can be used as a simple tool to compute the add-factors.
The debugging of the logical coherence of equations and data is carried out through a Residual Check procedure.
It consists of the following steps:
1. add another exogenous variable - the constant adjustment - to every equation of the model, both behavioral and technical identity: that can be done in BIMETS by using the ConstantAdjustment argument of the SIMULATE function, as in step 3;
2. fill in with the estimated residuals all the constant adjustments for the behavioral equations, and fill in with zeroes the constant adjustments for the technical identities: that can be done in BIMETS by using the SIMULATE procedure with the option simType='RESCHECK', then by analyzing and using the ConstantAdjustmentRESCHECK attribute of the simulated model, as in the following simulation in step 3.
3. perform a simulation of the model: that can be done in BIMETS by using the SIMULATE procedure with the option ConstantAdjustment=ConstantAdjustmentRESCHECK;
4. compute the difference between the historical and the simulated values for all the endogenous variables;
5. check whether all the differences assessed in step 4 are zero in whole time range, eventually accounting for the error autocorrelation in behaviorals.
An example on ConstantAdjustmentRESCHECK usage is available at the end of the SIMULATE help page;
If a perfect tracking of the history is obtained, then the equations have been written coherently with the data, otherwise a simulated equation not tracking the historical values is an unambiguous symptom of data inconsistent with the model definition.
Aside from the residual check, the add-factors constitute an important tool to significantly improve the accuracy of forecasts made through an econometric model. Considering the following model:
the add-factors can be interpreted as estimates of the disturbance terms' future values or as adjustments of the intercepts in each equation. These add-factors round out the forecasts, by summarizing the effects of all the systematic factors not included in the model. One choice for the computation of the add-factors is given by past estimation residuals and past forecast errors or by an average of these errors.
Please note that, in the case of equation that presents an LHS function, the add-factor will be added before the application of the inverse function, i.e., during the simulation, the following:
will be solved as:
If a linear dependence between the simulated endogenous and the add-factor is preferred, users can manually insert an auxiliary equation into the model definition, e.g. the following:
can be replaced by:
During the simulation, the add-factors (if requested by the user) will be applied as in the following:
given as add-factors and the linear dependence from and .
| RATIONAL EXPECTATIONS MODELS |
BIMETS classifies a model as a forward-looking model if any model equation contains the TSLEAD time series function. Forward-looking models assume that economic agents have complete knowledge of an economic system and calculate the future value of economic variables correctly according to that knowledge. Thus, forward-looking models are called also rational expectations models and, in macro-econometric models, model-consistent expectations.
In forward-looking models, simulation complexity arises, and all simulation periods must be solved simultaneously because equations can contain references to past and future values. Thus, given N simulation periods requested by the user, each model equation must be replicated N-1 times and modified before the simulation takes place, accounting for lead transformations. Finally, the extended model must be simulated as a single block of equations.
Internal data structures too, such as the incidence and the Jacobian matrix, and the reordering arrays vpre and vblocks (described later in the "The Optimal Reordering" section), grow with the number of simulation periods requested by the user. Therefore, they can only be calculated when a new simulation is requested rather than when the model MDL definition is parsed, further extending computational time in simulation.
A simulation that spans several decades in a forward-looking models with hundreds of equations is not feasible in BIMETS. For a real scenario in a rational expectations model, see "Computational details and capabilities" section in the "US Federal Reserve quarterly model (FRB/US) in R with bimets" vignette.
To understand BIMETS internals when dealing with forward-looking models, please consider the following simple example of a forward-looking model having a single identity:
IDENTITY> Y EQ> Y = TSLEAD(Y) - TSLAG(Y) + X
Given X as an exogenous variable, if the requested simulation has a TSRANGE that spans two periods, then the model will be internally transformed into something like:
IDENTITY> Y EQ> Y = Y__LEAD__1 - TSLAG(Y) + X IDENTITY> Y__LEAD__1 EQ> Y__LEAD__1 = TSLEAD(Y,2) - Y + TSLEAD(X)
Accordingly, the model will be simulated only on the first period of the TSRANGE. Please note that TSLAG(Y) in the first equation, and TSLEAD(Y,2) in the second equation, are a kind of exogenous variables and must be defined in order for the simulation to be completed. Moreover, Y and Y__LEAD__1 are simultaneously involved in the iterative simulation algorithm, and both depend on each other, as also stated in the incidence matrix for the extended model:
$incidence_matrix
Y Y__LEAD__1
Y 0 1
Y__LEAD__1 1 0
Due to the mechanism described above, only DYNAMIC simulations are allowed in forward-looking models. See examples below, for a Klein-like forward-looking model simulation.
| THE OPTIMAL REORDERING |
In fact, the simulation process takes advantage of an appropriate equations reordering to increase the performances by iteratively solving only one subset of equations, while the others are solved straightforwardly. "...a different ordering of the equations can substantially affect the speed of convergence of the algorithm; indeed some orderings may produce divergence. The less feedback there is, the better the chances for fast convergence..." - Don, Gallo - Solving large sparse systems of equations in econometric models - Journal of Forecasting 1987.
For backward-looking models, the LOAD_MODEL function builds the model's incidence matrix, then defines the proper equations reordering. The incidence matrix is built from the equations of the model; it is a square matrix in which each row and each column represent an endogenous variable. If the (i,j) element is equal to 1 then in the model definition the current value of the endogenous variable referred by the i-row depends directly from the current value of the endogenous variable referred by the j-column. The reader can see an incidence matrix example in the section "BIMETS package" of this manual wherein the content of the kleinModel$incidence_matrix variable is printed out.
In econometric models, the incidence matrix is usually very sparse. Only a few of the total set of endogenous variables are used in each equation. In this situation, ordering the equation in a particular sequence will lead to a sensible reduction of the number of iterations needed to achieve convergence. Reordering the equations is equivalent to rearranging rows and columns of the incidence matrix. In this way, the incidence matrix might be made lower triangular for a subset of the equations.
For this subset, an endogenous variable determined in a specific equation has no incidence in any equation above it, although the same variable might have incidence in equations below it. Such a subset of equations is called recursive. Recursive systems are easy to solve. It is only necessary to solve each equation once if this is done in the proper order. On the other hand, it is unlikely for whole model to be recursive. Indeed the incidence graph is often cyclic, as in the Klein's model that presents the following circular dependecies in the incidence matrix: p <- w1 <- y <- i <- p as shown in the "BIMETS package" section figure.
For some subsets of the equations, some 1's will occur in the upper triangle of the incidence matrix for all possible orderings. Such subsets of equations are called simultaneous. To solve the endogenous variables in the simultaneous subset of equations, an iterative algorithm has to be used. Nevertheless, the equations in a simultaneous subset may be ordered so that the pattern of the 1's in the upper triangle forms a spike. The variables corresponding to the 1's in the upper triangle are called feedback variables.
A qualitative graphical example of an ordered incidence matrix is given in the following figure. The white areas are all 0's, the gray areas contain 0's and 1's. The 1's in the light gray areas refer to variables already evaluated in previous subset of equations, therefore they are known terms within the current subset. The 1's in the dark gray areas refer to variables evaluated within the subset.
In BIMETS, the final pattern of an incidence matrix after the equations reordering generally features N+1 blocks:
- One recursive subset of equation, i.e. the pre-recursive VPRE in image;
- N blocks of equations, VBLOCK in image, each built with a simultaneous VSIM and a post-recursive VPOST subset of equations;
As said, the pre-recursive and the post-recursive subsets are lower triangular. Therefore the corresponding equations are solvable with a cascade substitution with no iteration. Only the simultaneous subsets need an iterative algorithm to be solved. It is important to say that the convergence criterion may also be applied to feedback variables only: when the feedback variables converge, the rest of the simultaneous variables also do.
BIMETS builds and analyzes the model's incidence matrix, and then it i) computes the strongly connected component of the related incidence graph by using the Tarjan algorithm (Ref: Tarjan, Robert - Depth-first search and linear graph algorithms - SIAM Journal on Computing - June 1972), and ii) orders the equations in pre-recursive and, for each block of equations, in simultaneous and post-recursive subsets. The simultaneous subsets are then analyzed in order to find a minimal set of feedback variables. This last problem is known to be NP-complete (Ref: Garey, Johnson - Computers and Intractability: a Guide to the Theory of NP-completeness - San Francisco, Freeman 1979).
The optimal reordering of the model equations is programmatically achieved through the use of an iterative algorithm applied to the incidence matrix that can produce 1+3*N ordered lists of endogenous variables, respectively:
1. One list vpre that is the ordered list containing the names of the endogenous pre-recursive variables to be sequentially computed (once per simulation period) before the simulation iterative algorithm takes place;
2. For each of the N elements in the vblocks list:
2.1 One list vsim (the simultaneous subset) that is the ordered list containing the names of the endogenous variables to be sequentially computed during each iteration of the simulation iterative algorithm;
2.2 One list vfeed that is the list containing the names of the endogenous feedback variables; generally vfeed are the last variables in the ordered vsim list in the sambe block;
2.3. One list vpost that is the ordered list containing the names of the endogenous post-recursive variables to be sequentially computed (once per simulation period) after the simulation iterative algorithm has found a solution in the previous simultaneous subset in the same block;
Once equations are reordered, the previous conceptual scheme is modified as follows:
1. initialize the solution for the current simulation period;
2. compute the pre-recursive equations (i.e. the equation of the endogenous variables in the vpre ordered list);
For each block in vblocks:
3.1 iteratively compute the system of simultaneous equations (i.e. the equation of the endogenous variables in the vsim ordered list): for each iteration: i) update the values of the current endogenous variables, ii) update the feedback variables accordingly to the simulation algorithm in use (see next section for details on simulation algorithms) and iii) verify that the convergence criterion is satisfied on the feedback variables vfeed or that the maximum number of iterations has been reached;
3.2 compute the post-recursive equations (i.e. the equation of the endogenous variables in the vpost ordered list);
Finally:
4. save the solutions;
Clearly, each endogenous variable is updated accordingly to its related equation EQ> in the MDL model definition.
In forward-looking models, the incidence matrix and the equations reordering depend on the simulation periods count, therefore the model attributes incidence_matrix, vblocks, and vpre are calculated only after a simulation has been initialized, and will be available to users in the model$simulation[['__SIM_PARAMETERS__']] lists.
The reader can see an equations reordering example in the section "BIMETS package" of this manual wherein the content of the kleinModel$vpre and kleinModel$vblocks variables are printed out.
| THE SIMULATION ALGORITHMS |
Given the -exogenous variable, , and the -endogenous variable in a simultaneous subset, at the iteration , with the position of the equation in a reordered model, the modified Gauss-Seidel method takes for the approximation of the endogenous variable the solution of the following:
Newton-Raphson's methods can be seen as an extension of the modified Gauss-Seidel algorithm, and a further step is required: in Newton-Raphson, feedback variables are updated not by using their model equations, but by using the inverse of the Jacobian matrix and the following assignment:
given the vector of feedback variables values at iteration , the identity matrix , and the Jacobian matrix , with and equal to the number of feedback variables for the given block of equations. Please note that the modified Gauss-Seidel algorithm can be seen as a reduced form of a Netwotn algorithm, given .
In Newton-Raphson methods, the Jacobian matrix is calculated as follows:
1 - shock the feedback variables one at a time by a small amount;
2 - for each shocked feedback variable, evaluate the shocked solution of the simultaneous subset in the current block;
3 - calculate the derivatives (i.e. the column in the Jacobian matrix related to the shocked feedback variable) using the difference quotients between the shocked and the base solution of the simultaneous subset.
As said, the convergence is always tested at each iteration's end on the feedback variables.
Newton-Raphson methods on a reordered model require the calculation of the Jacobian matrix on the feedback endogenous variables, i.e. at least iterations per simulation period, with as the number of feedback variables. For large models (i.e. more than 30 feedback variables) if the overall required convergence is greater than the speedup over the Gauss-Seidel method is small or negative, if the Jacobian matrix is recalculated at each iteration. Moreover, the Gauss-Seidel method does not require a matrix inversion; therefore, it is more robust against algebraical and numerical issues. For small models, both methods are fast on modern computers. On the other hand, Gausse-Seidel fails to find a convergence for a small set of econometric models, even when a convergence exists. In general, given a system of equations , with and , the Gauss-Seidel algorithm is known to converge if either:
- is symmetric positive-definite;
- is strictly or irreducibly diagonally dominant.
To improve simulation speed, BIMETS evaluates the Newton-Raphson algorithm's performance during simulation, and, at each iteration, a new Jacobian matrix is calculated only if the convergence speed is slower than a predefined threshold. In a vectorized simulation (e.g., STOCHSIMULATE, OPTIMIZE, RENORM), if simAlgo="NEWTON" the Jacobian matrix is calculated only on the unperturbed model, then applied to all realizations; if simAlgo="FULLNEWTON" a new Jacobian matrix is calculated for each realization.
The simulation of a non-trivial model, if computed by using the same data but on different hardware, software or numerical libraries, produces numerical differences. Therefore a convergence criterion smaller than frequently leads to a local solution.
See Numerical methods for simulation and optimal control of large-scale macroeconomic models - Gabay, Nepomiastchy, Rachidi, Ravelli - 1980 for further information.
For more realistic scenarios, several advanced econometric exercises on the US Federal Reserve FRB/US econometric model (e.g., dynamic simulation in a monetary policy shock, rational expectations, endogenous targeting, stochastic simulation, etc.) are available in the "US Federal Reserve quarterly model (FRB/US) in R with bimets" vignette.
SIMULATE( model=NULL, simAlgo='GAUSS-SEIDEL', TSRANGE=NULL, simType='DYNAMIC', simConvergence=0.01, simIterLimit=100, ZeroErrorAC=FALSE, BackFill=0, Exogenize=NULL, ConstantAdjustment=NULL, verbose=FALSE, verboseSincePeriod=0, verboseVars=NULL, MULTMATRIX=FALSE, RENORM=FALSE, TARGET=NULL, INSTRUMENT=NULL, MM_SHOCK=0.00001, STOCHSIMULATE=FALSE, StochStructure=NULL, StochReplica=100, StochSeed=NULL, OPTIMIZE=FALSE, OptimizeBounds=NULL, OptimizeRestrictions=NULL, OptimizeFunctions=NULL, quietly=FALSE, RESCHECKeqList=NULL, JACOBIAN_SHOCK=1e-4, JacobianDrop=NULL, forceForwardLooking=FALSE, avoidCompliance=FALSE, ...)SIMULATE( model=NULL, simAlgo='GAUSS-SEIDEL', TSRANGE=NULL, simType='DYNAMIC', simConvergence=0.01, simIterLimit=100, ZeroErrorAC=FALSE, BackFill=0, Exogenize=NULL, ConstantAdjustment=NULL, verbose=FALSE, verboseSincePeriod=0, verboseVars=NULL, MULTMATRIX=FALSE, RENORM=FALSE, TARGET=NULL, INSTRUMENT=NULL, MM_SHOCK=0.00001, STOCHSIMULATE=FALSE, StochStructure=NULL, StochReplica=100, StochSeed=NULL, OPTIMIZE=FALSE, OptimizeBounds=NULL, OptimizeRestrictions=NULL, OptimizeFunctions=NULL, quietly=FALSE, RESCHECKeqList=NULL, JACOBIAN_SHOCK=1e-4, JacobianDrop=NULL, forceForwardLooking=FALSE, avoidCompliance=FALSE, ...)
model |
The BIMETS model object to be simulated. The simulation requires that all the model behaviorals, if any, have been previously estimated: all the behavioral coefficients (i.e. the regression coefficients and the autoregression coefficients for the errors, if any) must be numerically defined in the model object. (see also |
simAlgo |
The simulation algorithm to be used to solve the system of model equations for each time period in the simulation |
TSRANGE |
The time range of the simulation, as a four dimensional numerical array, |
simType |
The simulation type requested: |
simConvergence |
The percentage convergence value requested for the iterative process, which stops when the percentage difference of all the feedback variables between iterations is less than |
simIterLimit |
The value representing the maximum number of iterations to be performed. The iterative procedure will stop when |
ZeroErrorAC |
If |
BackFill |
Defined as an |
Exogenize |
A named list that specifies the endogenous variables to be exogenized. During the simulation and inside the provided time range, the exogenized endogenous variables will be assigned to their historical values. List names must be the names of the endogenous variables to be exogenized; each element of this list contains the time range of the exogenization for the related endogenous variable, in the form of a 4-dimensional integer array, i.e. start_year, start_period, end_year, end_period. A list element can also be assigned |
ConstantAdjustment |
A named list that specifies the constant adjustments (i.e. add-factors) to be added to the selected equations of the model. Each constant adjustment can be see as a new exogenous variable added to the equation of the specified endogenous variable. The list names are the names of the involved endogenous variables; each element of this is list contains the time series to be added to the equation of the related endogenous variable. Each provided time series must verify the compliance control check defined in |
verbose |
If |
verboseSincePeriod |
An integer that activates the verbose output, during the iterative process, only after the provided number of simulation periods |
verboseVars |
A |
MULTMATRIX |
It is |
RENORM |
It is |
TARGET |
see |
INSTRUMENT |
see |
MM_SHOCK |
see |
STOCHSIMULATE |
It is |
StochStructure |
The |
StochReplica |
An integer value that sets the number of stochastic simulation replications to be performed. See |
StochSeed |
A number used to initialize the pseudo-random number generator. It can be useful in order to replicate stochastic results. See |
OPTIMIZE |
It is |
OptimizeBounds |
see |
OptimizeRestrictions |
see |
OptimizeFunctions |
see |
quietly |
If |
RESCHECKeqList |
If |
JACOBIAN_SHOCK |
The value of the shock added to feedback variables in the derivative calculation of the Jacobian matrix. The default value is |
JacobianDrop |
The array built with feedback variables names to be excluded from the Jacobian matrix calulation |
forceForwardLooking |
If |
avoidCompliance |
If |
... |
Backward compatibility |
This function will add a new named element simulation into the output BIMETS model object.
The new simulation element is a named list; the names of the simulation list are the names of the endogenous variables of the model; each element of the simulation list contains the simulated time series of the related endogenous variable (see example).
The simulation list also contains the '__SIM_PARAMETERS__' element that contains the arguments passed to the function call during the latest SIMULATE run, e.g. TSRANGE, symType, simConvergence, symIterLimit, Exogenize, etc.: this data can be helpful in order to replicate the simulation results.
In case of a simType='RESCHECK' simulation, a new named element ConstantAdjustmentRESCHECK will be added to the output model. This new element is populated with a list of time series that contains, for each endogenous variable, the tracking residuals time series such that, when using this tracking residuals as add-factors in simulation, the related equation will solve to the trajectory given, for that variable, by its historical data (see example).
MDLLOAD_MODELESTIMATESTOCHSIMULATEMULTMATRIXRENORMOPTIMIZETIMESERIESBIMETS indexingBIMETS configuration
#define model myModelDefinition<- "MODEL COMMENT> Klein Model 1 of the U.S. Economy COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1921 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data myModel<-LOAD_MODEL(modelText=myModelDefinition) myModel<-LOAD_MODEL_DATA(myModel,myModelData) #estimate model myModel<-ESTIMATE(myModel, quietly = TRUE) #DYNAMIC SIMULATION #simulate model myModel<-SIMULATE(myModel ,TSRANGE=c(1923,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ) # #Simulation: 100.00% #...SIMULATE OK #get simulated time series "cn" and "y" TABIT(myModel$simulation$cn) # # Date, Prd., myModel$simulation$cn # # 1923, 1 , 50.338 # 1924, 1 , 55.6994 # 1925, 1 , 56.7111 # ... # 1940, 1 , 66.7799 # 1941, 1 , 75.451 # TABIT(myModel$simulation$y) # # Date, Prd., myModel$simulation$y # # 1923, 1 , 56.0305 # 1924, 1 , 65.8526 # 1925, 1 , 64.265 # ... # 1940, 1 , 76.8049 # 1941, 1 , 93.4459 # #get latest simulation parameters print(myModel$simulation$'__SIM_PARAMETERS__') #$TSRANGE #[1] 1923 1 1941 1 # #$simType #[1] "DYNAMIC" # #$simConvergence #[1] 1e-05 # #$simIterLimit #[1] 100 # #$ZeroErrorAC #[1] FALSE # #...etc etc ######################################################## #RESCHECK SIMULATION #simulate model myModel<-SIMULATE(myModel ,simType='RESCHECK' ,TSRANGE=c(1923,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ) # #Simulation: 100.00% #...SIMULATE OK #get consumption simulated vs historical differences TABIT(myModel$simulation$cn-myModel$modelData$cn) # # Date, Prd., myModel$simulation$cn - myModel$modelData$cn # # 1923, 1 , 1.56574 # 1924, 1 , 0.493503 # 1925, 1 , -0.0076079 # ... # 1939, 1 , -0.989201 # 1940, 1 , -0.785077 # 1941, 1 , 2.17345 # ######################################################## #FORECAST GNP in 1942 and 1943 #we need to extend exogenous variables in 1942 and 1943 myModel$modelData$w2 <- TSEXTEND(myModel$modelData$w2, UPTO=c(1943,1)) myModel$modelData$t <- TSEXTEND(myModel$modelData$t, UPTO=c(1943,1)) myModel$modelData$g <- TSEXTEND(myModel$modelData$g, UPTO=c(1943,1)) myModel$modelData$time <- TSEXTEND(myModel$modelData$time,UPTO=c(1943,1) ,EXTMODE='LINEAR') #simulate model myModel<-SIMULATE(myModel ,simType='FORECAST' ,TSRANGE=c(1940,1,1943,1) ,simConvergence=0.00001 ,simIterLimit=100 ) # #Simulation: 100.00% #...SIMULATE OK #get forecasted GNP TABIT(myModel$simulation$y) # # Date, Prd., myModel$simulation$y # # 1940, 1 , 74.5781 # 1941, 1 , 94.0153 # 1942, 1 , 133.969 # 1943, 1 , 199.913 # ######################################################## #VERBOSE SIMULATION myModel<-SIMULATE(myModel ,TSRANGE=c(1923,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ,verbose=TRUE ,verboseSincePeriod=19 ,verboseVars=c('cn') ) ######################################################## #DYNAMIC NEWTON SIMULATION #WITH EXOGENIZATION AND CONSTANT ADJUSTMENTS #define exogenization list #'cn' exogenized in 1923-1925 #'i' exogenized in whole TSRANGE exogenizeList<-list( cn = c(1923,1,1925,1), i = TRUE ) #define add-factors list constantAdjList<-list( cn = TIMESERIES(1,-1,START=c(1923,1),FREQ='A'), y = TIMESERIES(0.1,-0.1,-0.5,START=c(1926,1),FREQ='A') ) #simulate model myModel<-SIMULATE(myModel ,simAlgo='NEWTON' ,simType='DYNAMIC' ,TSRANGE=c(1923,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ,Exogenize=exogenizeList ,ConstantAdjustment=constantAdjList ) #SIMULATE(): endogenous variable "cn" has been exogenized from (trunc) ... #SIMULATE(): endogenous variable "i" has been exogenized from (trunc) ... #SIMULATE(): endogenous variable "cn" has a constant adjustment from (trunc) ... #SIMULATE(): endogenous variable "y" has a constant adjustment from (trunc) ... # #Simulation: 100.00% #...SIMULATE OK ######################################################## #EXAMPLE OF MODEL THAT FAILS GAUSS CONVERGENCE #define model myNewtonModelDefinition<- " MODEL COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1922 1 1931 1 EQ> cn = a1 + a2*p + a3*LAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1922 1 1931 1 EQ> i = b1 + b2*p + b3*LAG(p,1) + b4*LAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1922 1 1931 1 EQ> w1 = c1 + c2*(z+y+t-w2) + c3*LAG(z+y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Simple copy of y in z IDENTITY> z EQ> z = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = z + y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = LAG(k,1) + i END " #add data to model myModelData$z <- myModelData$y myNewtonModel<-LOAD_MODEL(modelText=myNewtonModelDefinition) myNewtonModel<-LOAD_MODEL_DATA(myNewtonModel,myModelData) #estimate model myNewtonModel<-ESTIMATE(myNewtonModel, quietly = TRUE) #GAUSS simulation fails to converge... myNewtonModel <- SIMULATE(myNewtonModel, TSRANGE = c(1921, 1, 1930, 1), simConvergence = 1e-7) #...while NEWTON converges myNewtonModel <- SIMULATE(myNewtonModel, simAlgo='NEWTON', TSRANGE = c(1921, 1, 1930, 1), simConvergence = 1e-7) ######################################################## #EXAMPLE OF MODEL THAT REQUIRES #A VARIABLE EXCLUSION FROM JACOBIAN MATRIX #define model myNewtonWithDropModelDefinition<- " MODEL COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1922 1 1931 1 EQ> cn = a1 + a2*p + a3*LAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1922 1 1931 1 EQ> i = b1 + b2*p + b3*LAG(p,1) + b4*LAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1922 1 1931 1 EQ> w1 = c1 + c2*(z+y+t-w2) + c3*LAG(z+y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Simple copy of y in z IDENTITY> z EQ> z = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = z + y - (w1+w2) IF> y < 0 COMMENT> Capital Stock IDENTITY> k EQ> k = LAG(k,1) + i END " #add data to model myModelData$z <- myModelData$y myNewtonModel <- LOAD_MODEL(modelText=myNewtonWithDropModelDefinition) myNewtonModel <- LOAD_MODEL_DATA(myNewtonModel,myModelData) #estimate model myNewtonModel <- ESTIMATE(myNewtonModel, quietly = TRUE) #"p" variable must be removed from Jacobian because of unverified IF> myNewtonModel <- SIMULATE(myNewtonModel, simAlgo='NEWTON', JacobianDrop='p', TSRANGE = c(1921, 1, 1930, 1), simConvergence = 1e-7) ######################################################## #COMPARE FORECAST IN 3 ALTERNATIVE #EXOGENOUS SCENARIOS #define model myModelDefinition <- "MODEL COMMENT> Klein Model 1 of the U.S. Economy COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1921 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data myModel <- LOAD_MODEL(modelText=myModelDefinition) myModel <- LOAD_MODEL_DATA(myModel,myModelData) #estimate model myModel <- ESTIMATE(myModel, quietly = TRUE) #create 3 new models for the 3 scenarios modelScenario1 <- myModel modelScenario2 <- myModel modelScenario3 <- myModel #scenario 1, define exogenous paths modelScenario1$modelData <- within(modelScenario1$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1943,1)) t = TSEXTEND(t, UPTO=c(1943,1)) g = TSEXTEND(g, UPTO=c(1943,1)) time = TSEXTEND(time,UPTO=c(1943,1) ,EXTMODE='LINEAR') }) #scenario 2, define exogenous paths modelScenario2$modelData <- within(modelScenario2$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1943,1)) t = TSEXTEND(t, UPTO=c(1943,1)) g = TSEXTEND(g, UPTO=c(1943,1) ,EXTMODE='LINEAR') time = TSEXTEND(time,UPTO=c(1943,1) ,EXTMODE='LINEAR') }) #scenario 3, define exogenous paths #we also change consumption cn add-factor modelScenario3$modelData <- within(modelScenario3$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1943,1) ,EXTMODE='MEAN4') t = TSEXTEND(t, UPTO=c(1943,1)) g = TSEXTEND(g, UPTO=c(1943,1) ,EXTMODE='LINEAR') time = TSEXTEND(time,UPTO=c(1943,1) ,EXTMODE='LINEAR') }) constantAdjListScenario3 <- constantAdjList constantAdjListScenario3$cn[[1941,1]] <- c(1,2,3) #simulate the 3 models modelScenario1 <- SIMULATE(modelScenario1 ,simAlgo='NEWTON' ,simType='FORECAST' ,TSRANGE=c(1940,1,1943,1) ,simConvergence=1e-5 ,simIterLimit=20) modelScenario2 <- SIMULATE(modelScenario2 ,simAlgo='NEWTON' ,simType='FORECAST' ,TSRANGE=c(1940,1,1943,1) ,simConvergence=1e-5 ,simIterLimit=20) modelScenario3 <- SIMULATE(modelScenario3 ,simAlgo='NEWTON' ,simType='FORECAST' ,TSRANGE=c(1940,1,1943,1) ,simConvergence=1e-5 ,simIterLimit=20 ,ConstantAdjustment = constantAdjListScenario3 ) #compare results on GNP TABIT(modelScenario1$simulation$y, modelScenario2$simulation$y, modelScenario3$simulation$y) ######################################################## #EXAMPLE OF MODEL'S TRACKING RESIDUALS INITIALIZATION BY USING #THE RESCHECK SIMULATION'S OUTPUT VALUE "ConstantAdjusmentRESCHECK" #define the model with LHS funs myModel<-'MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> LHS functions on EQ COMMENT> Exp Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> EXP(cn) = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Log Investment BEHAVIORAL> i TSRANGE 1925 1 1941 1 EQ> LOG(i) = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(TSDELTA(y)+t-w2) + c3*TSLAG(TSDELTA(y)+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Delta Gross National Product IDENTITY> y EQ> TSDELTA(y) = EXP(cn) + LOG(i) + g - t COMMENT> Profits IDENTITY> p EQ> p = TSDELTA(y) - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + LOG(i) IF> LOG(i) > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> LOG(i) <= 0 END' #define model data modelData<-list( cn=TSERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3, 57.8,55,50.9,45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g=TSERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4, 10.7,10.2,9.3,10,10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i=TSERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4, -6.2,-5.1,-3,-1.3,2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k=TSERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4, 207.6,210.6,215.7,216.7,213.3,207.1,202, 199,197.7,199.8,201.8,199.9,201.2,204.5,209.4, START=c(1920,1),FREQ=1), p=TSERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1, 21.7,15.6,11.4,7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1=TSERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2, 41.3,37.9,34.5,29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y=TSERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67, 57.7,50.7,41.3,45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t=TSERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5, 8.3,5.4,6.8,7.2,8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time=TSERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2, 3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2=TSERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2, 4.8,5.3,5.6,6,6.1,7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #example data transformation modelData<-within(modelData,{ i=exp(i); #we have LOG(i) in the model MDL definition cn=log(cn); #we have EXP(cn) in the model MDL definition y=CUMSUM(y) #we have TSDELTA(y) in the model MDL definition }) #load model and model data model<-LOAD_MODEL(modelText=myModel) model<-LOAD_MODEL_DATA(model,modelData) #estimate model model<-ESTIMATE(model) #get initial tracking residuals in range 1925-1935 #we need to set ZeroErrorAC to TRUE due to error autocorrelation #in Consumption MDL definition model<-SIMULATE(model, TSRANGE=c(1925,1,1935,1), simType='RESCHECK', ZeroErrorAC=TRUE) #get init trac initTrac<-model$ConstantAdjustmentRESCHECK #dynamic simulation using initTrac as constant adjustments #we remove first two periods from simulation range #due to error autocorrelation in Consumption MDL equation model<-SIMULATE(model, TSRANGE=c(1927,1,1935,1), ConstantAdjustment=initTrac) #check simulated values are equals to historical ones in simulation range for (idxV in model$vendog) { print(max(abs(model$simulation[[idxV]]- TSPROJECT(model$modelData[[idxV]],TSRANGE=c(1927,1,1935,1))))) } ######################################################## #EXAMPLE OF FORWARD-LOOKING KLEIN-LIKE MODEL #HAVING RATIONAL EXPECTATION ON INVESTMENTS #define model kleinLeadModelDefinition<- "MODEL COMMENT> Klein Model 1 of the U.S. Economy COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment with TSLEAD IDENTITY> i EQ> i = (MOVAVG(i,2)+TSLEAD(i))/2 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END" #define model data kleinLeadModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data kleinLeadModel<-LOAD_MODEL(modelText=kleinLeadModelDefinition) kleinLeadModel<-LOAD_MODEL_DATA(kleinLeadModel,kleinLeadModelData) #estimate model kleinLeadModel<-ESTIMATE(kleinLeadModel, quietly = TRUE) #set expected value of 2 for Investment in 1931 #(note that simulation TSRANGE spans up to 1930) kleinLeadModel$modelData$i[[1931,1]]<-2 #simulate model kleinLeadModel<-SIMULATE(kleinLeadModel ,TSRANGE=c(1924,1,1930,1)) #print simulated investments TABIT(kleinLeadModel$simulation$i)#define model myModelDefinition<- "MODEL COMMENT> Klein Model 1 of the U.S. Economy COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1921 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data myModel<-LOAD_MODEL(modelText=myModelDefinition) myModel<-LOAD_MODEL_DATA(myModel,myModelData) #estimate model myModel<-ESTIMATE(myModel, quietly = TRUE) #DYNAMIC SIMULATION #simulate model myModel<-SIMULATE(myModel ,TSRANGE=c(1923,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ) # #Simulation: 100.00% #...SIMULATE OK #get simulated time series "cn" and "y" TABIT(myModel$simulation$cn) # # Date, Prd., myModel$simulation$cn # # 1923, 1 , 50.338 # 1924, 1 , 55.6994 # 1925, 1 , 56.7111 # ... # 1940, 1 , 66.7799 # 1941, 1 , 75.451 # TABIT(myModel$simulation$y) # # Date, Prd., myModel$simulation$y # # 1923, 1 , 56.0305 # 1924, 1 , 65.8526 # 1925, 1 , 64.265 # ... # 1940, 1 , 76.8049 # 1941, 1 , 93.4459 # #get latest simulation parameters print(myModel$simulation$'__SIM_PARAMETERS__') #$TSRANGE #[1] 1923 1 1941 1 # #$simType #[1] "DYNAMIC" # #$simConvergence #[1] 1e-05 # #$simIterLimit #[1] 100 # #$ZeroErrorAC #[1] FALSE # #...etc etc ######################################################## #RESCHECK SIMULATION #simulate model myModel<-SIMULATE(myModel ,simType='RESCHECK' ,TSRANGE=c(1923,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ) # #Simulation: 100.00% #...SIMULATE OK #get consumption simulated vs historical differences TABIT(myModel$simulation$cn-myModel$modelData$cn) # # Date, Prd., myModel$simulation$cn - myModel$modelData$cn # # 1923, 1 , 1.56574 # 1924, 1 , 0.493503 # 1925, 1 , -0.0076079 # ... # 1939, 1 , -0.989201 # 1940, 1 , -0.785077 # 1941, 1 , 2.17345 # ######################################################## #FORECAST GNP in 1942 and 1943 #we need to extend exogenous variables in 1942 and 1943 myModel$modelData$w2 <- TSEXTEND(myModel$modelData$w2, UPTO=c(1943,1)) myModel$modelData$t <- TSEXTEND(myModel$modelData$t, UPTO=c(1943,1)) myModel$modelData$g <- TSEXTEND(myModel$modelData$g, UPTO=c(1943,1)) myModel$modelData$time <- TSEXTEND(myModel$modelData$time,UPTO=c(1943,1) ,EXTMODE='LINEAR') #simulate model myModel<-SIMULATE(myModel ,simType='FORECAST' ,TSRANGE=c(1940,1,1943,1) ,simConvergence=0.00001 ,simIterLimit=100 ) # #Simulation: 100.00% #...SIMULATE OK #get forecasted GNP TABIT(myModel$simulation$y) # # Date, Prd., myModel$simulation$y # # 1940, 1 , 74.5781 # 1941, 1 , 94.0153 # 1942, 1 , 133.969 # 1943, 1 , 199.913 # ######################################################## #VERBOSE SIMULATION myModel<-SIMULATE(myModel ,TSRANGE=c(1923,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ,verbose=TRUE ,verboseSincePeriod=19 ,verboseVars=c('cn') ) ######################################################## #DYNAMIC NEWTON SIMULATION #WITH EXOGENIZATION AND CONSTANT ADJUSTMENTS #define exogenization list #'cn' exogenized in 1923-1925 #'i' exogenized in whole TSRANGE exogenizeList<-list( cn = c(1923,1,1925,1), i = TRUE ) #define add-factors list constantAdjList<-list( cn = TIMESERIES(1,-1,START=c(1923,1),FREQ='A'), y = TIMESERIES(0.1,-0.1,-0.5,START=c(1926,1),FREQ='A') ) #simulate model myModel<-SIMULATE(myModel ,simAlgo='NEWTON' ,simType='DYNAMIC' ,TSRANGE=c(1923,1,1941,1) ,simConvergence=0.00001 ,simIterLimit=100 ,Exogenize=exogenizeList ,ConstantAdjustment=constantAdjList ) #SIMULATE(): endogenous variable "cn" has been exogenized from (trunc) ... #SIMULATE(): endogenous variable "i" has been exogenized from (trunc) ... #SIMULATE(): endogenous variable "cn" has a constant adjustment from (trunc) ... #SIMULATE(): endogenous variable "y" has a constant adjustment from (trunc) ... # #Simulation: 100.00% #...SIMULATE OK ######################################################## #EXAMPLE OF MODEL THAT FAILS GAUSS CONVERGENCE #define model myNewtonModelDefinition<- " MODEL COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1922 1 1931 1 EQ> cn = a1 + a2*p + a3*LAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1922 1 1931 1 EQ> i = b1 + b2*p + b3*LAG(p,1) + b4*LAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1922 1 1931 1 EQ> w1 = c1 + c2*(z+y+t-w2) + c3*LAG(z+y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Simple copy of y in z IDENTITY> z EQ> z = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = z + y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = LAG(k,1) + i END " #add data to model myModelData$z <- myModelData$y myNewtonModel<-LOAD_MODEL(modelText=myNewtonModelDefinition) myNewtonModel<-LOAD_MODEL_DATA(myNewtonModel,myModelData) #estimate model myNewtonModel<-ESTIMATE(myNewtonModel, quietly = TRUE) #GAUSS simulation fails to converge... myNewtonModel <- SIMULATE(myNewtonModel, TSRANGE = c(1921, 1, 1930, 1), simConvergence = 1e-7) #...while NEWTON converges myNewtonModel <- SIMULATE(myNewtonModel, simAlgo='NEWTON', TSRANGE = c(1921, 1, 1930, 1), simConvergence = 1e-7) ######################################################## #EXAMPLE OF MODEL THAT REQUIRES #A VARIABLE EXCLUSION FROM JACOBIAN MATRIX #define model myNewtonWithDropModelDefinition<- " MODEL COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1922 1 1931 1 EQ> cn = a1 + a2*p + a3*LAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1922 1 1931 1 EQ> i = b1 + b2*p + b3*LAG(p,1) + b4*LAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1922 1 1931 1 EQ> w1 = c1 + c2*(z+y+t-w2) + c3*LAG(z+y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Simple copy of y in z IDENTITY> z EQ> z = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = z + y - (w1+w2) IF> y < 0 COMMENT> Capital Stock IDENTITY> k EQ> k = LAG(k,1) + i END " #add data to model myModelData$z <- myModelData$y myNewtonModel <- LOAD_MODEL(modelText=myNewtonWithDropModelDefinition) myNewtonModel <- LOAD_MODEL_DATA(myNewtonModel,myModelData) #estimate model myNewtonModel <- ESTIMATE(myNewtonModel, quietly = TRUE) #"p" variable must be removed from Jacobian because of unverified IF> myNewtonModel <- SIMULATE(myNewtonModel, simAlgo='NEWTON', JacobianDrop='p', TSRANGE = c(1921, 1, 1930, 1), simConvergence = 1e-7) ######################################################## #COMPARE FORECAST IN 3 ALTERNATIVE #EXOGENOUS SCENARIOS #define model myModelDefinition <- "MODEL COMMENT> Klein Model 1 of the U.S. Economy COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1921 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data myModel <- LOAD_MODEL(modelText=myModelDefinition) myModel <- LOAD_MODEL_DATA(myModel,myModelData) #estimate model myModel <- ESTIMATE(myModel, quietly = TRUE) #create 3 new models for the 3 scenarios modelScenario1 <- myModel modelScenario2 <- myModel modelScenario3 <- myModel #scenario 1, define exogenous paths modelScenario1$modelData <- within(modelScenario1$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1943,1)) t = TSEXTEND(t, UPTO=c(1943,1)) g = TSEXTEND(g, UPTO=c(1943,1)) time = TSEXTEND(time,UPTO=c(1943,1) ,EXTMODE='LINEAR') }) #scenario 2, define exogenous paths modelScenario2$modelData <- within(modelScenario2$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1943,1)) t = TSEXTEND(t, UPTO=c(1943,1)) g = TSEXTEND(g, UPTO=c(1943,1) ,EXTMODE='LINEAR') time = TSEXTEND(time,UPTO=c(1943,1) ,EXTMODE='LINEAR') }) #scenario 3, define exogenous paths #we also change consumption cn add-factor modelScenario3$modelData <- within(modelScenario3$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1943,1) ,EXTMODE='MEAN4') t = TSEXTEND(t, UPTO=c(1943,1)) g = TSEXTEND(g, UPTO=c(1943,1) ,EXTMODE='LINEAR') time = TSEXTEND(time,UPTO=c(1943,1) ,EXTMODE='LINEAR') }) constantAdjListScenario3 <- constantAdjList constantAdjListScenario3$cn[[1941,1]] <- c(1,2,3) #simulate the 3 models modelScenario1 <- SIMULATE(modelScenario1 ,simAlgo='NEWTON' ,simType='FORECAST' ,TSRANGE=c(1940,1,1943,1) ,simConvergence=1e-5 ,simIterLimit=20) modelScenario2 <- SIMULATE(modelScenario2 ,simAlgo='NEWTON' ,simType='FORECAST' ,TSRANGE=c(1940,1,1943,1) ,simConvergence=1e-5 ,simIterLimit=20) modelScenario3 <- SIMULATE(modelScenario3 ,simAlgo='NEWTON' ,simType='FORECAST' ,TSRANGE=c(1940,1,1943,1) ,simConvergence=1e-5 ,simIterLimit=20 ,ConstantAdjustment = constantAdjListScenario3 ) #compare results on GNP TABIT(modelScenario1$simulation$y, modelScenario2$simulation$y, modelScenario3$simulation$y) ######################################################## #EXAMPLE OF MODEL'S TRACKING RESIDUALS INITIALIZATION BY USING #THE RESCHECK SIMULATION'S OUTPUT VALUE "ConstantAdjusmentRESCHECK" #define the model with LHS funs myModel<-'MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> LHS functions on EQ COMMENT> Exp Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> EXP(cn) = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Log Investment BEHAVIORAL> i TSRANGE 1925 1 1941 1 EQ> LOG(i) = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(TSDELTA(y)+t-w2) + c3*TSLAG(TSDELTA(y)+t-w2,1)+c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Delta Gross National Product IDENTITY> y EQ> TSDELTA(y) = EXP(cn) + LOG(i) + g - t COMMENT> Profits IDENTITY> p EQ> p = TSDELTA(y) - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + LOG(i) IF> LOG(i) > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> LOG(i) <= 0 END' #define model data modelData<-list( cn=TSERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3, 57.8,55,50.9,45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g=TSERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4, 10.7,10.2,9.3,10,10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i=TSERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4, -6.2,-5.1,-3,-1.3,2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k=TSERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4, 207.6,210.6,215.7,216.7,213.3,207.1,202, 199,197.7,199.8,201.8,199.9,201.2,204.5,209.4, START=c(1920,1),FREQ=1), p=TSERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1, 21.7,15.6,11.4,7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1=TSERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2, 41.3,37.9,34.5,29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y=TSERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67, 57.7,50.7,41.3,45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t=TSERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5, 8.3,5.4,6.8,7.2,8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time=TSERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2, 3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2=TSERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2, 4.8,5.3,5.6,6,6.1,7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #example data transformation modelData<-within(modelData,{ i=exp(i); #we have LOG(i) in the model MDL definition cn=log(cn); #we have EXP(cn) in the model MDL definition y=CUMSUM(y) #we have TSDELTA(y) in the model MDL definition }) #load model and model data model<-LOAD_MODEL(modelText=myModel) model<-LOAD_MODEL_DATA(model,modelData) #estimate model model<-ESTIMATE(model) #get initial tracking residuals in range 1925-1935 #we need to set ZeroErrorAC to TRUE due to error autocorrelation #in Consumption MDL definition model<-SIMULATE(model, TSRANGE=c(1925,1,1935,1), simType='RESCHECK', ZeroErrorAC=TRUE) #get init trac initTrac<-model$ConstantAdjustmentRESCHECK #dynamic simulation using initTrac as constant adjustments #we remove first two periods from simulation range #due to error autocorrelation in Consumption MDL equation model<-SIMULATE(model, TSRANGE=c(1927,1,1935,1), ConstantAdjustment=initTrac) #check simulated values are equals to historical ones in simulation range for (idxV in model$vendog) { print(max(abs(model$simulation[[idxV]]- TSPROJECT(model$modelData[[idxV]],TSRANGE=c(1927,1,1935,1))))) } ######################################################## #EXAMPLE OF FORWARD-LOOKING KLEIN-LIKE MODEL #HAVING RATIONAL EXPECTATION ON INVESTMENTS #define model kleinLeadModelDefinition<- "MODEL COMMENT> Klein Model 1 of the U.S. Economy COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1921 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 COMMENT> Investment with TSLEAD IDENTITY> i EQ> i = (MOVAVG(i,2)+TSLEAD(i))/2 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1921 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock IDENTITY> k EQ> k = TSLAG(k,1) + i END" #define model data kleinLeadModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model and model data kleinLeadModel<-LOAD_MODEL(modelText=kleinLeadModelDefinition) kleinLeadModel<-LOAD_MODEL_DATA(kleinLeadModel,kleinLeadModelData) #estimate model kleinLeadModel<-ESTIMATE(kleinLeadModel, quietly = TRUE) #set expected value of 2 for Investment in 1931 #(note that simulation TSRANGE spans up to 1930) kleinLeadModel$modelData$i[[1931,1]]<-2 #simulate model kleinLeadModel<-SIMULATE(kleinLeadModel ,TSRANGE=c(1924,1,1930,1)) #print simulated investments TABIT(kleinLeadModel$simulation$i)
The STOCHSIMULATE operation performs a stochastic simulation. The simulation algorithms are the same as those used by the SIMULATE operation.
Forecasts produced by structural econometric models are subject to several sources of error, such as random disturbance term of each stochastic equation, errors in estimated coefficients, errors in forecasts of exogenous variables, errors in preliminary data and mis-specification of the model.
The forecast error depending on the structural disturbances can be analyzed by using the stochastic simulation procedure.
The deterministic simulation is the simultaneous solution of an econometric model obtained by applying, for each stochastic (behavioral) equation, the expected values of the structural disturbances, which are all zero by assumption. In the BIMETS STOCHSIMULATE stochastic simulation, the structural disturbances are given values that have specified stochastic properties. The error terms of the estimated behavioral equation of the model are appropriately perturbed. Identity equations and exogenous variables can be as well perturbed by disturbances that have specified stochastic properties. The model is then solved for each data set with different values of the disturbances. Finally, mean and standard deviation are computed for each simulated endogenous variable.
In terms of computational efficiency, the procedure takes advantage of the fact that multiple datasets are bound together in matrices. Therefore, to achieve a global convergence, the iterative simulation algorithm is executed once for all perturbed datasets. This solution can be viewed as a sort of a SIMD (i.e. Single Instruction Multiple Data) parallel simulation: the STOCHSIMULATE function transforms time series into matrices and consequently can easily bind multiple datasets by column. At the same time, a single run ensures a fast code execution. Finally, each column in the output matrices represents a stochastic realization.
By using the StochStructure argument of this function, users can define a stochastic structure for the disturbances. For each variable of the model, users can provide a distinct probability distribution for the disturbance, and a specific time range of application. Mean and standard deviation for each simulated endogenous time series will be stored in the stochastic_simulation element of the output model object; all the stochastic realizations will be stored in the simulation_MM element of the output model object as named matrices.
In the following figure, the advanced Klein model (see code example), has been perturbed during the forecast operation by applying a normal disturbance to the endogenous Consumption behavioral cn add-factor in year 1942, and a uniform disturbance to the exogenous Government Expenditure time series g along all the simulation TSRANGE. The normal disturbance applied to the cn behavioral has a zero mean and a standard deviation equal to the behavioral regression standard error,
i.e. advancedKleinModel$behaviorals$cn$statistics$StandardErrorRegression, thus roughly replicating the ESTIMATE regression error during the current perturbation (not accounting for inter-equations cross-covariance).
At the moment, all the disturbances are i.i.d. and are not transformed into a congruent autoregressive scheme in the case the related perturbed endogenous behavioral presents an autocorrelation for the errors in its MDL definition, e.g. ERROR> AUTO(n)
For more realistic scenarios, several advanced econometric exercises on the US Federal Reserve FRB/US econometric model (e.g., dynamic simulation in a monetary policy shock, rational expectations, endogenous targeting, stochastic simulation, etc.) are available in the "US Federal Reserve quarterly model (FRB/US) in R with bimets" vignette.
STOCHSIMULATE(model=NULL, simAlgo='GAUSS-SEIDEL', TSRANGE=NULL, simType='DYNAMIC', simConvergence=0.01, simIterLimit=100, ZeroErrorAC=FALSE, BackFill=0, Exogenize=NULL, ConstantAdjustment=NULL, verbose=FALSE, verboseSincePeriod=0, verboseVars=NULL, StochStructure=NULL, StochReplica=100, StochSeed=NULL, quietly=FALSE, RESCHECKeqList=NULL, JACOBIAN_SHOCK=1e-4, JacobianDrop=NULL, forceForwardLooking=FALSE, avoidCompliance=FALSE, ...)STOCHSIMULATE(model=NULL, simAlgo='GAUSS-SEIDEL', TSRANGE=NULL, simType='DYNAMIC', simConvergence=0.01, simIterLimit=100, ZeroErrorAC=FALSE, BackFill=0, Exogenize=NULL, ConstantAdjustment=NULL, verbose=FALSE, verboseSincePeriod=0, verboseVars=NULL, StochStructure=NULL, StochReplica=100, StochSeed=NULL, quietly=FALSE, RESCHECKeqList=NULL, JACOBIAN_SHOCK=1e-4, JacobianDrop=NULL, forceForwardLooking=FALSE, avoidCompliance=FALSE, ...)
model |
see |
simAlgo |
see |
TSRANGE |
see |
simType |
see |
simConvergence |
see |
simIterLimit |
see |
ZeroErrorAC |
see |
BackFill |
see |
Exogenize |
see |
ConstantAdjustment |
see |
verbose |
see |
verboseSincePeriod |
see |
verboseVars |
see |
StochStructure |
the named
StochStructure =
list(
var_name1 = list(
TSRANGE=...,
TYPE=...,
PARS=...),
var_name2 = list(...)
...
var_nameN = list(...)
)
ENDOGENOUS REFERENCE.
$MDL Klein GDP equation
EQ> y = cn + i + g - t
$STOCHSIMULATE argument
StochStructure =
list(
y = list(
TSRANGE=TRUE,
TYPE='NORM',
PARS=c(0,1))
)
then, during the stochastic simulation, the following assignment will be evaluated in the whole simulation y <- ( ConstantAdjustment$y + rnorm(...,0,1) ) + cn + i + g - t EXOGENOUS REFERENCE.
$MDL Klein GDP equation
EQ> y = cn + i + g - t
$STOCHSIMULATE argument
StochStructure =
list(
g = list(
TSRANGE=TRUE,
TYPE='UNIF',
PARS=c(-1,1))
)
then, during the stochastic simulation, the following assignment will be evaluated in the whole simulation y <- ConstantAdjustment$y + cn + i + ( g + runif(...,-1,1) ) - t If the generic name
$MDL equation
EQ> y = cn + i + g - t
$STOCHSIMULATE argument
StochStructure =
list(
g = list(
TSRANGE=myTSRANGE,
TYPE='MATRIX',
PARS=userMatrix)
)
then, during the stochastic simulation, the following assignment will be evaluated only in the sub-range y <- ConstantAdjustment$y + cn + i + ( userMatrix ) - t with - |
StochReplica |
an integer value that sets the number of stochastic realizations to be produced |
StochSeed |
a number used to initialize the pseudo-random number generator. It can be helpful in order to replicate stochastic results |
quietly |
see |
RESCHECKeqList |
see |
JACOBIAN_SHOCK |
see |
JacobianDrop |
see |
forceForwardLooking |
see |
avoidCompliance |
see |
... |
see |
This function will add, into the output BIMETS model object, three new named elements, respectively stochastic_simulation, simulation_MM and INSTRUMENT_MM.
The stochastic_simulation element is a named list(), having endogenous variables as names. Each element will contain two time series: the mean and the standard deviation of the related stochastic simulated endogenous time series.
The arguments passed to the function call during the latest STOCHSIMULATE run will be inserted into the '__STOCH_SIM_PARAMETERS__' element of the stochastic_simulation list; this data can be helpful in order to replicate the stochastic simulation results.
The simulation_MM element is a named list(), having the endogenous variables as names. Each element will contain an R x C matrix, given R the number of observations in the simulation TSRANGE and C=1+StochReplica. The first column of each matrix contains the related endogenous variable's unperturbed simulated values; the remaining columns will contain all the StochReplica stochastic realizations for the related endogenous variable (see example).
The INSTRUMENT_MM element is a named list(), having INSTRUMENT variables as names. Each element will contain an R x C matrix, given R the number of observations in the simulation TSRANGE and C=1+StochReplica. The first column of each matrix contains the related INSTRUMENT variable's unperturbed values; the remaining columns will contain all the StochReplica stochastic realizations for the related INSTRUMENT variable.
MDLLOAD_MODELESTIMATESIMULATERENORMOPTIMIZETIMESERIESBIMETS indexingBIMETS configuration
#define the advanced Klein model advancedKleinModelDef <- " MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and COMMENT> conditional equation evaluations COMMENT> Consumption with autocorrelation on errors BEHAVIORAL> cn TSRANGE 1923 1 1940 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment with restrictions BEHAVIORAL> i TSRANGE 1923 1 1940 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor with PDL BEHAVIORAL> w1 TSRANGE 1923 1 1940 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 2 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with IF switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END " #load the model advancedKleinModel <- LOAD_MODEL(modelText = advancedKleinModelDef) #define data kleinModelData <- list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8, 55,50.9,45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7, 10.2,9.3,10,10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2, -5.1,-3,-1.3,2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6, 210.6,215.7,216.7,213.3,207.1,202,199,197.7,199.8, 201.8,199.9,201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7, 15.6,11.4,7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3, 37.9,34.5,29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7, 50.7,41.3,45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4, 6.8,7.2,8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time=TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0, 1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8, 5.3,5.6,6,6.1,7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ); #load time series into the model object advancedKleinModel <- LOAD_MODEL_DATA(advancedKleinModel, kleinModelData) #estimate the model advancedKleinModel <- ESTIMATE(advancedKleinModel, quietly=TRUE) #we want to perform a stochastic forecast of the GNP up to 1944 #we will add normal disturbances to endogenous Consumption 'cn' #in 1942 by using its regression standard error #we will add uniform disturbances to exogenous Government Expenditure 'g' #in whole TSRANGE myStochStructure <- list( cn=list( TSRANGE=c(1942,1,1942,1), TYPE='NORM', PARS=c(0,advancedKleinModel$behaviorals$cn$statistics$StandardErrorRegression) ), g=list( TSRANGE=TRUE, TYPE='UNIF', PARS=c(-1,1) ) ) #we need to extend exogenous variables up to 1944 advancedKleinModel$modelData <- within(advancedKleinModel$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1944,1),EXTMODE='CONSTANT') t = TSEXTEND(t, UPTO=c(1944,1),EXTMODE='LINEAR') g = TSEXTEND(g, UPTO=c(1944,1),EXTMODE='CONSTANT') k = TSEXTEND(k, UPTO=c(1944,1),EXTMODE='LINEAR') time = TSEXTEND(time,UPTO=c(1944,1),EXTMODE='LINEAR') }) #stochastic model forecast advancedKleinModel <- STOCHSIMULATE(advancedKleinModel ,simType='FORECAST' ,TSRANGE=c(1941,1,1944,1) ,StochStructure=myStochStructure ,StochSeed=123 ) #print mean and standard deviation of forecasted GNP with(advancedKleinModel$stochastic_simulation,TABIT(y$mean, y$sd)) # Date, Prd., y$mean , y$sd # # 1941, 1 , 125.5045 , 4.250935 # 1942, 1 , 173.2946 , 9.2632 # 1943, 1 , 185.9602 , 11.87774 # 1944, 1 , 141.0807 , 11.6973 #print the unperturbed forecasted GNP along with the #first 5 perturbed realizations with(advancedKleinModel$simulation_MM,print(y[,1:6])) #################################################### #EXAMPLE WITH TYPE='MATRIX' TSRANGE <- c(1935,1,1940,1) StochReplica <- 100 #we will perturb simulation by using regression residuals #get cn and i residuals in TSRANGE cn_residuals <- TSPROJECT(advancedKleinModel$behaviorals$cn$residuals, TSRANGE=TSRANGE, ARRAY = TRUE) i_residuals <- TSPROJECT(advancedKleinModel$behaviorals$i$residuals, TSRANGE=TSRANGE, ARRAY = TRUE) #define stochastic matrices cn_matrix <- c() i_matrix <- c() #populate matrices for (idx in 1:StochReplica) { rand <- rnorm(1,0,1) cn_matrix <- cbind(cn_matrix,rand*cn_residuals) i_matrix <- cbind(i_matrix,rand*i_residuals) } #define stochastic structure myStochStructure <- list( cn=list( TSRANGE=TRUE, TYPE='MATRIX', PARS=cn_matrix ), i=list( TSRANGE=TRUE, TYPE='MATRIX', PARS=i_matrix ) ) #stochastic simulation advancedKleinModel <- STOCHSIMULATE(advancedKleinModel ,TSRANGE=TSRANGE ,StochStructure=myStochStructure ) #print GNP mean and sd with(advancedKleinModel$stochastic_simulation,TABIT(y$mean, y$sd)) ######################################################### #EXAMPLE OF MODEL THAT REQUIRES THE FULL NEWTON ALGORITHM #see profit equation myFullNewtonDefinition<- "MODEL COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1922 1 1929 1 EQ> cn = a1 + a2*p + a3*LAG(p,1) + a4*(w1+w2+w3) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1922 1 1929 1 EQ> i = b1 + b2*p + b3*LAG(p,1) + b4*LAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1922 1 1929 1 EQ> w1 = c1 + c2*(z+y+t-w2) + c3*LAG(z+y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Demand for Labor BEHAVIORAL> w3 TSRANGE 1922 1 1929 1 EQ> w3 = c1 + c2*(z+y+t-w2) + c3*LAG(z+y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t IDENTITY> z EQ> z = cn + i + g - t COMMENT> Profits with cubic dependence on cn IDENTITY> p EQ> p = cn^3/1000 + z + y - (w1+w2+w3) COMMENT> Capital Stock IDENTITY> k EQ> k = LAG(k,1) + i END " #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #add data to model myModelData$z <- myModelData$y myModelData$w3 <- (myModelData$w1) myFullNewtonModel <- LOAD_MODEL(modelText=myFullNewtonDefinition) myFullNewtonModel <- LOAD_MODEL_DATA(myFullNewtonModel,myModelData) myFullNewtonModel <- ESTIMATE(myFullNewtonModel) #simple Newton will fail, due to #large variance in normal disturbances #...while full Newton will converge myFullNewtonModel <- STOCHSIMULATE(myFullNewtonModel, simAlgo='FULLNEWTON', TSRANGE = c(1921, 1, 1923, 1), simConvergence = 1e-5, simIterLimit = 250, StochReplica = 100, StochSeed=123, StochStructure = list( cn=list( TSRANGE=TRUE, TYPE='NORM', PARS=c(0,20) ) ) ,verbose=TRUE )#define the advanced Klein model advancedKleinModelDef <- " MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and COMMENT> conditional equation evaluations COMMENT> Consumption with autocorrelation on errors BEHAVIORAL> cn TSRANGE 1923 1 1940 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment with restrictions BEHAVIORAL> i TSRANGE 1923 1 1940 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor with PDL BEHAVIORAL> w1 TSRANGE 1923 1 1940 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 2 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with IF switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END " #load the model advancedKleinModel <- LOAD_MODEL(modelText = advancedKleinModelDef) #define data kleinModelData <- list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8, 55,50.9,45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7, 10.2,9.3,10,10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2, -5.1,-3,-1.3,2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6, 210.6,215.7,216.7,213.3,207.1,202,199,197.7,199.8, 201.8,199.9,201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7, 15.6,11.4,7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3, 37.9,34.5,29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7, 50.7,41.3,45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4, 6.8,7.2,8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time=TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0, 1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8, 5.3,5.6,6,6.1,7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ); #load time series into the model object advancedKleinModel <- LOAD_MODEL_DATA(advancedKleinModel, kleinModelData) #estimate the model advancedKleinModel <- ESTIMATE(advancedKleinModel, quietly=TRUE) #we want to perform a stochastic forecast of the GNP up to 1944 #we will add normal disturbances to endogenous Consumption 'cn' #in 1942 by using its regression standard error #we will add uniform disturbances to exogenous Government Expenditure 'g' #in whole TSRANGE myStochStructure <- list( cn=list( TSRANGE=c(1942,1,1942,1), TYPE='NORM', PARS=c(0,advancedKleinModel$behaviorals$cn$statistics$StandardErrorRegression) ), g=list( TSRANGE=TRUE, TYPE='UNIF', PARS=c(-1,1) ) ) #we need to extend exogenous variables up to 1944 advancedKleinModel$modelData <- within(advancedKleinModel$modelData,{ w2 = TSEXTEND(w2, UPTO=c(1944,1),EXTMODE='CONSTANT') t = TSEXTEND(t, UPTO=c(1944,1),EXTMODE='LINEAR') g = TSEXTEND(g, UPTO=c(1944,1),EXTMODE='CONSTANT') k = TSEXTEND(k, UPTO=c(1944,1),EXTMODE='LINEAR') time = TSEXTEND(time,UPTO=c(1944,1),EXTMODE='LINEAR') }) #stochastic model forecast advancedKleinModel <- STOCHSIMULATE(advancedKleinModel ,simType='FORECAST' ,TSRANGE=c(1941,1,1944,1) ,StochStructure=myStochStructure ,StochSeed=123 ) #print mean and standard deviation of forecasted GNP with(advancedKleinModel$stochastic_simulation,TABIT(y$mean, y$sd)) # Date, Prd., y$mean , y$sd # # 1941, 1 , 125.5045 , 4.250935 # 1942, 1 , 173.2946 , 9.2632 # 1943, 1 , 185.9602 , 11.87774 # 1944, 1 , 141.0807 , 11.6973 #print the unperturbed forecasted GNP along with the #first 5 perturbed realizations with(advancedKleinModel$simulation_MM,print(y[,1:6])) #################################################### #EXAMPLE WITH TYPE='MATRIX' TSRANGE <- c(1935,1,1940,1) StochReplica <- 100 #we will perturb simulation by using regression residuals #get cn and i residuals in TSRANGE cn_residuals <- TSPROJECT(advancedKleinModel$behaviorals$cn$residuals, TSRANGE=TSRANGE, ARRAY = TRUE) i_residuals <- TSPROJECT(advancedKleinModel$behaviorals$i$residuals, TSRANGE=TSRANGE, ARRAY = TRUE) #define stochastic matrices cn_matrix <- c() i_matrix <- c() #populate matrices for (idx in 1:StochReplica) { rand <- rnorm(1,0,1) cn_matrix <- cbind(cn_matrix,rand*cn_residuals) i_matrix <- cbind(i_matrix,rand*i_residuals) } #define stochastic structure myStochStructure <- list( cn=list( TSRANGE=TRUE, TYPE='MATRIX', PARS=cn_matrix ), i=list( TSRANGE=TRUE, TYPE='MATRIX', PARS=i_matrix ) ) #stochastic simulation advancedKleinModel <- STOCHSIMULATE(advancedKleinModel ,TSRANGE=TSRANGE ,StochStructure=myStochStructure ) #print GNP mean and sd with(advancedKleinModel$stochastic_simulation,TABIT(y$mean, y$sd)) ######################################################### #EXAMPLE OF MODEL THAT REQUIRES THE FULL NEWTON ALGORITHM #see profit equation myFullNewtonDefinition<- "MODEL COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1922 1 1929 1 EQ> cn = a1 + a2*p + a3*LAG(p,1) + a4*(w1+w2+w3) COEFF> a1 a2 a3 a4 COMMENT> Investment BEHAVIORAL> i TSRANGE 1922 1 1929 1 EQ> i = b1 + b2*p + b3*LAG(p,1) + b4*LAG(k,1) COEFF> b1 b2 b3 b4 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1922 1 1929 1 EQ> w1 = c1 + c2*(z+y+t-w2) + c3*LAG(z+y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Demand for Labor BEHAVIORAL> w3 TSRANGE 1922 1 1929 1 EQ> w3 = c1 + c2*(z+y+t-w2) + c3*LAG(z+y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t IDENTITY> z EQ> z = cn + i + g - t COMMENT> Profits with cubic dependence on cn IDENTITY> p EQ> p = cn^3/1000 + z + y - (w1+w2+w3) COMMENT> Capital Stock IDENTITY> k EQ> k = LAG(k,1) + i END " #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #add data to model myModelData$z <- myModelData$y myModelData$w3 <- (myModelData$w1) myFullNewtonModel <- LOAD_MODEL(modelText=myFullNewtonDefinition) myFullNewtonModel <- LOAD_MODEL_DATA(myFullNewtonModel,myModelData) myFullNewtonModel <- ESTIMATE(myFullNewtonModel) #simple Newton will fail, due to #large variance in normal disturbances #...while full Newton will converge myFullNewtonModel <- STOCHSIMULATE(myFullNewtonModel, simAlgo='FULLNEWTON', TSRANGE = c(1921, 1, 1923, 1), simConvergence = 1e-5, simIterLimit = 250, StochReplica = 100, StochSeed=123, StochStructure = list( cn=list( TSRANGE=TRUE, TYPE='NORM', PARS=c(0,20) ) ) ,verbose=TRUE )
This function prints basic information about a BIMETS model, e.g. behaviorals and identities count, coefficients count, the presence of estimated coefficients or simulated time series.
## S3 method for class 'BIMETS_MODEL' summary(object,...) ## S3 method for class 'BIMETS_MODEL' print(x,...)## S3 method for class 'BIMETS_MODEL' summary(object,...) ## S3 method for class 'BIMETS_MODEL' print(x,...)
object |
A BIMET model. |
x |
A BIMET model. |
... |
Arguments list for the generic method. |
This function prints basic information about a BIMETS model, i.e.:
- the name of the model;
- the behaviorals count;
- the identities count;
- the coefficients count;
- the check for the compliance of the model data;
- the check for the coefficients definition in all the behaviorals;
- the check for the definition of a simulated time series for each related endogenous variable of the model;
MDLLOAD_MODELSIMULATEMULTMATRIXRENORMTIMESERIESBIMETS indexingBIMETS configuration
#define model myModelDefinition<- "MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment BEHAVIORAL> i TSRANGE 1923 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model myModel<-LOAD_MODEL(modelText=myModelDefinition) #model summary summary(myModel) #BIMETS MODEL #----------------------------------- #name: myModelDefinition #behaviorals: 3 #identities: 3 #coefficients: 12 #model data: not OK #.CHECK_MODEL_DATA(): model has no data. Please use LOAD_MODEL_DATA(). #fully estimated: FALSE #simulated: FALSE #load data into the model myModel<-LOAD_MODEL_DATA(myModel,myModelData,showWarnings = TRUE) #estimate the model myModel<-ESTIMATE(myModel) #model summary print(myModel) #BIMETS MODEL #----------------------------------- #name: myModelDefinition #behaviorals: 3 #identities: 3 #coefficients: 12 #model data: OK #fully estimated: TRUE #simulated: FALSE#define model myModelDefinition<- "MODEL COMMENT> Modified Klein Model 1 of the U.S. Economy with PDL, COMMENT> autocorrelation on errors, restrictions and conditional evaluations COMMENT> Consumption BEHAVIORAL> cn TSRANGE 1925 1 1941 1 EQ> cn = a1 + a2*p + a3*TSLAG(p,1) + a4*(w1+w2) COEFF> a1 a2 a3 a4 ERROR> AUTO(2) COMMENT> Investment BEHAVIORAL> i TSRANGE 1923 1 1941 1 EQ> i = b1 + b2*p + b3*TSLAG(p,1) + b4*TSLAG(k,1) COEFF> b1 b2 b3 b4 RESTRICT> b2 + b3 = 1 COMMENT> Demand for Labor BEHAVIORAL> w1 TSRANGE 1925 1 1941 1 EQ> w1 = c1 + c2*(y+t-w2) + c3*TSLAG(y+t-w2,1) + c4*time COEFF> c1 c2 c3 c4 PDL> c3 1 3 COMMENT> Gross National Product IDENTITY> y EQ> y = cn + i + g - t COMMENT> Profits IDENTITY> p EQ> p = y - (w1+w2) COMMENT> Capital Stock with switches IDENTITY> k EQ> k = TSLAG(k,1) + i IF> i > 0 IDENTITY> k EQ> k = TSLAG(k,1) IF> i <= 0 END" #define model data myModelData<-list( cn =TIMESERIES(39.8,41.9,45,49.2,50.6,52.6,55.1,56.2,57.3,57.8,55,50.9, 45.6,46.5,48.7,51.3,57.7,58.7,57.5,61.6,65,69.7, START=c(1920,1),FREQ=1), g =TIMESERIES(4.6,6.6,6.1,5.7,6.6,6.5,6.6,7.6,7.9,8.1,9.4,10.7,10.2,9.3,10, 10.5,10.3,11,13,14.4,15.4,22.3, START=c(1920,1),FREQ=1), i =TIMESERIES(2.7,-.2,1.9,5.2,3,5.1,5.6,4.2,3,5.1,1,-3.4,-6.2,-5.1,-3,-1.3, 2.1,2,-1.9,1.3,3.3,4.9, START=c(1920,1),FREQ=1), k =TIMESERIES(182.8,182.6,184.5,189.7,192.7,197.8,203.4,207.6,210.6,215.7, 216.7,213.3,207.1,202,199,197.7,199.8,201.8,199.9, 201.2,204.5,209.4, START=c(1920,1),FREQ=1), p =TIMESERIES(12.7,12.4,16.9,18.4,19.4,20.1,19.6,19.8,21.1,21.7,15.6,11.4, 7,11.2,12.3,14,17.6,17.3,15.3,19,21.1,23.5, START=c(1920,1),FREQ=1), w1 =TIMESERIES(28.8,25.5,29.3,34.1,33.9,35.4,37.4,37.9,39.2,41.3,37.9,34.5, 29,28.5,30.6,33.2,36.8,41,38.2,41.6,45,53.3, START=c(1920,1),FREQ=1), y =TIMESERIES(43.7,40.6,49.1,55.4,56.4,58.7,60.3,61.3,64,67,57.7,50.7,41.3, 45.3,48.9,53.3,61.8,65,61.2,68.4,74.1,85.3, START=c(1920,1),FREQ=1), t =TIMESERIES(3.4,7.7,3.9,4.7,3.8,5.5,7,6.7,4.2,4,7.7,7.5,8.3,5.4,6.8,7.2, 8.3,6.7,7.4,8.9,9.6,11.6, START=c(1920,1),FREQ=1), time =TIMESERIES(NA,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10, START=c(1920,1),FREQ=1), w2 =TIMESERIES(2.2,2.7,2.9,2.9,3.1,3.2,3.3,3.6,3.7,4,4.2,4.8,5.3,5.6,6,6.1, 7.4,6.7,7.7,7.8,8,8.5, START=c(1920,1),FREQ=1) ) #load model myModel<-LOAD_MODEL(modelText=myModelDefinition) #model summary summary(myModel) #BIMETS MODEL #----------------------------------- #name: myModelDefinition #behaviorals: 3 #identities: 3 #coefficients: 12 #model data: not OK #.CHECK_MODEL_DATA(): model has no data. Please use LOAD_MODEL_DATA(). #fully estimated: FALSE #simulated: FALSE #load data into the model myModel<-LOAD_MODEL_DATA(myModel,myModelData,showWarnings = TRUE) #estimate the model myModel<-ESTIMATE(myModel) #model summary print(myModel) #BIMETS MODEL #----------------------------------- #name: myModelDefinition #behaviorals: 3 #identities: 3 #coefficients: 12 #model data: OK #fully estimated: TRUE #simulated: FALSE
This function prints, in a human-readable format, the content of a list of time series. Time series can be subsetted with the projection argument TSRANGE.
TABIT(..., TSRANGE=NULL, headers=NULL, digits=getOption('digits'), avoidCompliance=FALSE)TABIT(..., TSRANGE=NULL, headers=NULL, digits=getOption('digits'), avoidCompliance=FALSE)
... |
Input list of time series that must satisfy the compliance control check defined in |
TSRANGE |
The optional date range of data presentation. |
headers |
Optional column headers. |
digits |
Controls the number of digits to print out. Valid values are 1 to 22 with a default of 7. |
avoidCompliance |
If |
This function prints out time series data and returns a NULL value.
TSPROJECTMOVAVGTSDELTATSLAGTSPROJECTTSEXTENDTSLEAD
#create monthly series ts1<-TSERIES(INTS(1,15),START=c(2000,1),FREQ=12) ts2<-TSERIES(INTS(1,15),START=c(2001,1),FREQ=12) ts3<-TSERIES(rnorm(15),START=c(2002,1),FREQ=12) ts4<-TSERIES(rep(NA,15),START=c(2001,4),FREQ=12) TABIT(ts1,ts2,ts3,ts4) # print... # # Date, Prd., ts1 , ts2 , ts3 , ts4 # # Jan 2000, 1 , 1 , , , # Feb 2000, 2 , 2 , , , # Mar 2000, 3 , 3 , , , # ... # Dec 2000, 12 , 12 , , , # Jan 2001, 1 , 13 , 1 , , # Feb 2001, 2 , 14 , 2 , , # ... # Dec 2001, 12 , , 12 , , NA # Jan 2002, 1 , , 13 , -1.419782 , NA # Feb 2002, 2 , , 14 , -1.070188 , NA # Mar 2002, 3 , , 15 , 0.889571 , NA # Apr 2002, 4 , , , 0.9583392 , NA # ... # Feb 2003, 2 , , , -0.3444237 , # Mar 2003, 3 , , , -0.3073225 , #create quarterly series, set TSRANGE then print with 3 digits ts1<-TSERIES(INTS(1,15),START=c(2000,1),FREQ=4) ts2<-TSERIES(INTS(1,15),START=c(2001,1),FREQ=4) ts3<-TSERIES(rnorm(15),START=c(2002,1),FREQ=4) ts4<-TSERIES(rep(NA,15),START=c(2001,4),FREQ=4) TABIT(ts1,ts2,ts3,ts4,TSRANGE=c(1991,3,2003,2),digits=3) #print... # # Date, Prd., ts1 , ts2 , ts3 , ts4 # # 2000 Q1, 1 , 1 , , , # 2000 Q2, 2 , 2 , , , # 2000 Q3, 3 , 3 , , , # 2000 Q4, 4 , 4 , , , # 2001 Q1, 1 , 5 , 1 , , # 2001 Q2, 2 , 6 , 2 , , # 2001 Q3, 3 , 7 , 3 , , # 2001 Q4, 4 , 8 , 4 , , NA # 2002 Q1, 1 , 9 , 5 , 0.729 , NA # 2002 Q2, 2 , 10 , 6 , 0.923 , NA # 2002 Q3, 3 , 11 , 7 , -0.81 , NA # 2002 Q4, 4 , 12 , 8 , -0.0748 , NA # 2003 Q1, 1 , 13 , 9 , 0.248 , NA # 2003 Q2, 2 , 14 , 10 , -0.347 , NA #create daily series and set TSRANGE ts1<-TSERIES(INTS(1,25),START=c(2000,1),FREQ=366) ts2<-TSERIES(INTS(1,25),START=c(2000,10),FREQ=366) ts3<-TSERIES(rnorm(25),START=c(2000,20),FREQ=366) ts4<-TSERIES(rep(NA,25),START=c(2000,30),FREQ=366) TABIT(ts1,ts2,ts3,ts4,TSRANGE=c(2000,5,2000,35)) #...print data #headers TABIT(ts1,ts2,ts3,ts4, TSRANGE=c(2000,25,2000,35), headers=c('LOREM','IPSUM','DOLOR','SIT'))#create monthly series ts1<-TSERIES(INTS(1,15),START=c(2000,1),FREQ=12) ts2<-TSERIES(INTS(1,15),START=c(2001,1),FREQ=12) ts3<-TSERIES(rnorm(15),START=c(2002,1),FREQ=12) ts4<-TSERIES(rep(NA,15),START=c(2001,4),FREQ=12) TABIT(ts1,ts2,ts3,ts4) # print... # # Date, Prd., ts1 , ts2 , ts3 , ts4 # # Jan 2000, 1 , 1 , , , # Feb 2000, 2 , 2 , , , # Mar 2000, 3 , 3 , , , # ... # Dec 2000, 12 , 12 , , , # Jan 2001, 1 , 13 , 1 , , # Feb 2001, 2 , 14 , 2 , , # ... # Dec 2001, 12 , , 12 , , NA # Jan 2002, 1 , , 13 , -1.419782 , NA # Feb 2002, 2 , , 14 , -1.070188 , NA # Mar 2002, 3 , , 15 , 0.889571 , NA # Apr 2002, 4 , , , 0.9583392 , NA # ... # Feb 2003, 2 , , , -0.3444237 , # Mar 2003, 3 , , , -0.3073225 , #create quarterly series, set TSRANGE then print with 3 digits ts1<-TSERIES(INTS(1,15),START=c(2000,1),FREQ=4) ts2<-TSERIES(INTS(1,15),START=c(2001,1),FREQ=4) ts3<-TSERIES(rnorm(15),START=c(2002,1),FREQ=4) ts4<-TSERIES(rep(NA,15),START=c(2001,4),FREQ=4) TABIT(ts1,ts2,ts3,ts4,TSRANGE=c(1991,3,2003,2),digits=3) #print... # # Date, Prd., ts1 , ts2 , ts3 , ts4 # # 2000 Q1, 1 , 1 , , , # 2000 Q2, 2 , 2 , , , # 2000 Q3, 3 , 3 , , , # 2000 Q4, 4 , 4 , , , # 2001 Q1, 1 , 5 , 1 , , # 2001 Q2, 2 , 6 , 2 , , # 2001 Q3, 3 , 7 , 3 , , # 2001 Q4, 4 , 8 , 4 , , NA # 2002 Q1, 1 , 9 , 5 , 0.729 , NA # 2002 Q2, 2 , 10 , 6 , 0.923 , NA # 2002 Q3, 3 , 11 , 7 , -0.81 , NA # 2002 Q4, 4 , 12 , 8 , -0.0748 , NA # 2003 Q1, 1 , 13 , 9 , 0.248 , NA # 2003 Q2, 2 , 14 , 10 , -0.347 , NA #create daily series and set TSRANGE ts1<-TSERIES(INTS(1,25),START=c(2000,1),FREQ=366) ts2<-TSERIES(INTS(1,25),START=c(2000,10),FREQ=366) ts3<-TSERIES(rnorm(25),START=c(2000,20),FREQ=366) ts4<-TSERIES(rep(NA,25),START=c(2000,30),FREQ=366) TABIT(ts1,ts2,ts3,ts4,TSRANGE=c(2000,5,2000,35)) #...print data #headers TABIT(ts1,ts2,ts3,ts4, TSRANGE=c(2000,25,2000,35), headers=c('LOREM','IPSUM','DOLOR','SIT'))
This function returns the O-order, L-lag differences of the input time series.
TSDELTA(x = NULL, L = 1, O = 1, avoidCompliance = FALSE, ...)TSDELTA(x = NULL, L = 1, O = 1, avoidCompliance = FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
L |
Lag. |
O |
Order of the difference. |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a BIMETS time series.
TSDELTAPTSDELTALOGTSLAGMOVAVGINTSCUMSUM
#random TS n<-10 xArr<-rnorm(n) ts1<-TSERIES(xArr,START=c(2000,1),FREQ='A') TABIT(ts1,TSDELTA(ts1,1,1),TSDELTA(ts1,1,2),TSDELTA(ts1,1,3))#random TS n<-10 xArr<-rnorm(n) ts1<-TSERIES(xArr,START=c(2000,1),FREQ='A') TABIT(ts1,TSDELTA(ts1,1,1),TSDELTA(ts1,1,2),TSDELTA(ts1,1,3))
This function returns the L-lag logarithmic differences of the input time series.
TSDELTALOG(x = NULL, L = 1, avoidCompliance = FALSE, ...)TSDELTALOG(x = NULL, L = 1, avoidCompliance = FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
L |
Lag. |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a BIMETS time series.
#sequence TS n<-10 ts1<-TSERIES(1:n,START=c(2000,1),FREQ='A') TABIT(ts1,TSDELTALOG(ts1,1))#sequence TS n<-10 ts1<-TSERIES(1:n,START=c(2000,1),FREQ='A') TABIT(ts1,TSDELTALOG(ts1,1))
This function returns the O-order, L-lag percentage differences of the input time series.
If the input time series frequency is a multiple of the L lag argument, then it is possible to set the argument ANNUALIZE=TRUE in order to have the percent changes returned at annual rates, i.e. raised to the power of frequency/L.
TSDELTAP(x = NULL, L = 1, ANNUALIZE = FALSE, avoidCompliance = FALSE, ...)TSDELTAP(x = NULL, L = 1, ANNUALIZE = FALSE, avoidCompliance = FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
L |
Lag. |
ANNUALIZE |
If TRUE the percent changes are returned as annual rates, i.e. raised to the power of frequency/L |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a BIMETS time series.
#TS Q n<-10; ts1<-TSERIES(n:0,START=c(2000,1),FREQ='Q') TABIT(ts1,TSDELTAP(ts1,1)) #TS 366 ts1<-TSERIES(seq(1,length=10,by=-0.001),START=c(2000,1),FREQ=366) TABIT(ts1,TSDELTAP(ts1,1,ANNUALIZE=TRUE))#TS Q n<-10; ts1<-TSERIES(n:0,START=c(2000,1),FREQ='Q') TABIT(ts1,TSDELTAP(ts1,1)) #TS 366 ts1<-TSERIES(seq(1,length=10,by=-0.001),START=c(2000,1),FREQ=366) TABIT(ts1,TSDELTAP(ts1,1,ANNUALIZE=TRUE))
This function returns a time series that is compliant with BIMETS compliance control defined in is.bimets. Users can provide observation values, frequency, and the starting period. Moreover, users can provide metadata information that will be stored into the time series object as attributes.TIMESERIES is an alias for TSERIES.
TIMESERIES(..., START = c(2000,1), FREQ = 1, SOURCE = NULL, TITLE = NULL, UNITS = NULL, SCALEFAC = 0, class=NULL, avoidCompliance = FALSE) TSERIES(..., START = c(2000,1), FREQ = 1, SOURCE = NULL, TITLE = NULL, UNITS = NULL, SCALEFAC = 0, class=NULL, avoidCompliance = FALSE)TIMESERIES(..., START = c(2000,1), FREQ = 1, SOURCE = NULL, TITLE = NULL, UNITS = NULL, SCALEFAC = 0, class=NULL, avoidCompliance = FALSE) TSERIES(..., START = c(2000,1), FREQ = 1, SOURCE = NULL, TITLE = NULL, UNITS = NULL, SCALEFAC = 0, class=NULL, avoidCompliance = FALSE)
... |
List of values to be inserted into the output time series. This function accepts
arguments of class |
START |
This argument defines the start of the time series. Starting period can be specified as |
FREQ |
The frequency of the time series. Frequency can be |
SOURCE |
Set the metadata string that represents the source of the data. Metadata will be lost if the current time series is transformed by any function that changes its values. |
TITLE |
Set the metadata string that represents the description of the data. Metadata will be lost if the current time series is transformed by any function that changes its values. |
UNITS |
Set the metadata string that represents the unit of measure of the data. Metadata will be lost if the current time series is transformed by any function that changes its values. |
SCALEFAC |
Set the numerical value that represents the scale factor of the data. Users may eventually want to use this value in code. Metadata will be lost if the current time series is transformed by any function that changes its values. |
class |
If Please note that BIMETS package performs better with |
avoidCompliance |
If |
This function returns a BIMETS time series that is compliant with the BIMETS compliance control defined in is.bimets.
is.bimetsas.bimetsBIMETS indexingBIMETS configurationfromBIMETStoTSfromBIMETStoXTSNOELSTSDATESINTSTABIT
#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #create a simple R ts n<-10 ts1<-ts((1:n),start=c(2000,1),frequency=1) #create a bimets ts annual #having the following values: 5, (all data in ts1), NA, 8 #starting from Jan 2020, and having custom metadata out_tseries<-TIMESERIES(5,ts1,NA,8,START=c(2020,1),FREQ=1, SOURCE='mySource',TITLE='myTitle',UNITS='myUnits',SCALEFAC=2) #print out TABIT(out_tseries) #use Date() as start date TABIT(TIMESERIES(1:10,START=as.Date('2000-01-01'),FREQ='A')) TABIT(TIMESERIES(1:10,START=as.Date('2000-01-01'),FREQ='Y')) TABIT(TIMESERIES(1:10,START=as.Date('2000-07-08'),FREQ='D')) TABIT(TIMESERIES(1:10,START=as.Date('2018-01-01'),FREQ='W')) #use yearmon()/yearqtr() as start date TABIT(TIMESERIES(1:10,START=as.yearmon('Mar 2001'),FREQ='M')) TABIT(TIMESERIES(1:10,START=as.yearqtr('2000 Q3'),FREQ='Q')) #create ts monthly with metadata out_tseries<-TIMESERIES(5,ts1,NA,8,START=c(2020,1),FREQ='M', SOURCE='mySource',TITLE='myTitle',UNITS='myUnits',SCALEFAC=2) #print out TABIT(out_tseries) #create daily out_tseries<-TSERIES(5,ts1,NA,8,START=c(2000,1),FREQ=366, SOURCE='mySource',TITLE='myTitle',UNITS='myUnits',SCALEFAC=2) #print out TABIT(out_tseries) #insert values skipping 366 in non-bissextile myLength<-400 myValues<-1:myLength myDates<-as.Date('2001-01-01')+0:(myLength-1) ts<-as.bimets(xts(myValues,order.by = myDates)) TABIT(ts) #366 observation will be a duplicated of 365, see as.bimets() help#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #create a simple R ts n<-10 ts1<-ts((1:n),start=c(2000,1),frequency=1) #create a bimets ts annual #having the following values: 5, (all data in ts1), NA, 8 #starting from Jan 2020, and having custom metadata out_tseries<-TIMESERIES(5,ts1,NA,8,START=c(2020,1),FREQ=1, SOURCE='mySource',TITLE='myTitle',UNITS='myUnits',SCALEFAC=2) #print out TABIT(out_tseries) #use Date() as start date TABIT(TIMESERIES(1:10,START=as.Date('2000-01-01'),FREQ='A')) TABIT(TIMESERIES(1:10,START=as.Date('2000-01-01'),FREQ='Y')) TABIT(TIMESERIES(1:10,START=as.Date('2000-07-08'),FREQ='D')) TABIT(TIMESERIES(1:10,START=as.Date('2018-01-01'),FREQ='W')) #use yearmon()/yearqtr() as start date TABIT(TIMESERIES(1:10,START=as.yearmon('Mar 2001'),FREQ='M')) TABIT(TIMESERIES(1:10,START=as.yearqtr('2000 Q3'),FREQ='Q')) #create ts monthly with metadata out_tseries<-TIMESERIES(5,ts1,NA,8,START=c(2020,1),FREQ='M', SOURCE='mySource',TITLE='myTitle',UNITS='myUnits',SCALEFAC=2) #print out TABIT(out_tseries) #create daily out_tseries<-TSERIES(5,ts1,NA,8,START=c(2000,1),FREQ=366, SOURCE='mySource',TITLE='myTitle',UNITS='myUnits',SCALEFAC=2) #print out TABIT(out_tseries) #insert values skipping 366 in non-bissextile myLength<-400 myValues<-1:myLength myDates<-as.Date('2001-01-01')+0:(myLength-1) ts<-as.bimets(xts(myValues,order.by = myDates)) TABIT(ts) #366 observation will be a duplicated of 365, see as.bimets() help
This function extends the time series definition range by using the directives specified in the EXTMODE and FACTOR arguments.
TSEXTEND(x = NULL, BACKTO = NULL, UPTO = NULL, EXTMODE = "GROWTH", FACTOR = NA, avoidCompliance = FALSE, ...)TSEXTEND(x = NULL, BACKTO = NULL, UPTO = NULL, EXTMODE = "GROWTH", FACTOR = NA, avoidCompliance = FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
BACKTO |
Define the new start of the time series, which must be provided as |
UPTO |
Define the new end of the time series, which must be provided as |
EXTMODE |
It must be one of the following: |
FACTOR |
User-defined value used by some options of the |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a BIMETS time series built by extending the input time series.
TSLAGTSJOINTSMERGETSPROJECTCUMSUMINDEXNUMTSTRIM
n<-10; ts1<-TIMESERIES(1:n,START=c(2000,1),FREQ='A') ts2<-TSEXTEND(ts1,BACKTO=c(1990,1),UPTO=c(2020,1),EXTMODE='GROWTH4') TABIT(ts1,ts2) xArr<-c(0.5,5.6,4.8,3.8,7.3,9.9,7.8,3.7,8.2,10) ts1<-TIMESERIES(xArr,START=c(2000,1),FREQ='A') ts2<-TSEXTEND(ts1,BACKTO=c(1990,1),UPTO=c(2020,1),EXTMODE='QUADRATIC') TABIT(ts1,ts2) xArr<-(1:n) dateArr<-seq(as.Date('2000/12/31'),by='year',length=n) dataF<-data.frame(dateArr,xArr) ts1<-TIMESERIES(xArr,START=c(2000,1),FREQ='A') ts2<-TSEXTEND(ts1,BACKTO=c(1990,1),UPTO=c(2020,1),EXTMODE='MYRATE',FACTOR=2.5) TABIT(ts1,ts2)n<-10; ts1<-TIMESERIES(1:n,START=c(2000,1),FREQ='A') ts2<-TSEXTEND(ts1,BACKTO=c(1990,1),UPTO=c(2020,1),EXTMODE='GROWTH4') TABIT(ts1,ts2) xArr<-c(0.5,5.6,4.8,3.8,7.3,9.9,7.8,3.7,8.2,10) ts1<-TIMESERIES(xArr,START=c(2000,1),FREQ='A') ts2<-TSEXTEND(ts1,BACKTO=c(1990,1),UPTO=c(2020,1),EXTMODE='QUADRATIC') TABIT(ts1,ts2) xArr<-(1:n) dateArr<-seq(as.Date('2000/12/31'),by='year',length=n) dataF<-data.frame(dateArr,xArr) ts1<-TIMESERIES(xArr,START=c(2000,1),FREQ='A') ts2<-TSEXTEND(ts1,BACKTO=c(1990,1),UPTO=c(2020,1),EXTMODE='MYRATE',FACTOR=2.5) TABIT(ts1,ts2)
This function returns detailed information about the input time series list. The requested information is defined in the argument MODE.
TSINFO(..., MODE = NULL, avoidCompliance=FALSE)TSINFO(..., MODE = NULL, avoidCompliance=FALSE)
... |
Input time series list. Each time series must satisfy the compliance control check defined in |
MODE |
Select the information to be retrieved from the list of time series. |
avoidCompliance |
If |
This function returns an array built of the requested information about the input time series list. In the case of MODE=START2 or MODE=END2 the output will be of class matrix().
NOELSis.bimetsBIMETS indexingfromBIMETStoTSfromBIMETStoXTSGETYEARPERIODINTSTSLOOKTABIT
#create ts ts1<-TIMESERIES(INTS(1,10),START=c(2004,2),FREQ=2, UNITS='myUnits',TITLE='myTitle',SOURCE='mySource') ts2<-TIMESERIES(INTS(1,20),START=c(2006,3),FREQ=4,SCALEFAC=1) ts3<-TIMESERIES(INTS(1,30),START=c(2008,7),FREQ=12) print(TSINFO(ts1,ts2,ts3,MODE='STARTY')) #print ... c(2004,2006,2008) print(TSINFO(ts1,ts2,ts3,MODE='ENDP')) #print ... c(1,2,12) print(TSINFO(ts1,ts2,ts3,MODE='FREQ')) #print ... c(2,4,12) print(TSINFO(ts1,ts2,ts3,MODE='START2')) #print ... #[,1] [,2] #[1,] 2004 2 #[2,] 2006 3 #[3,] 2008 7 print(TSINFO(ts1,ts2,ts3,MODE='END')) #print ... c(2009.5, 2011.5, 2011.0) print(TSINFO(ts1,ts2,ts3,MODE='FACTOR')) #print ... c(0,1,0) print(TSINFO(ts1,ts2,ts3,MODE='UNITS')) #print ... c('myUnits','','')#create ts ts1<-TIMESERIES(INTS(1,10),START=c(2004,2),FREQ=2, UNITS='myUnits',TITLE='myTitle',SOURCE='mySource') ts2<-TIMESERIES(INTS(1,20),START=c(2006,3),FREQ=4,SCALEFAC=1) ts3<-TIMESERIES(INTS(1,30),START=c(2008,7),FREQ=12) print(TSINFO(ts1,ts2,ts3,MODE='STARTY')) #print ... c(2004,2006,2008) print(TSINFO(ts1,ts2,ts3,MODE='ENDP')) #print ... c(1,2,12) print(TSINFO(ts1,ts2,ts3,MODE='FREQ')) #print ... c(2,4,12) print(TSINFO(ts1,ts2,ts3,MODE='START2')) #print ... #[,1] [,2] #[1,] 2004 2 #[2,] 2006 3 #[3,] 2008 7 print(TSINFO(ts1,ts2,ts3,MODE='END')) #print ... c(2009.5, 2011.5, 2011.0) print(TSINFO(ts1,ts2,ts3,MODE='FACTOR')) #print ... c(0,1,0) print(TSINFO(ts1,ts2,ts3,MODE='UNITS')) #print ... c('myUnits','','')
This function returns the join of the two input time series. If the first time series overlaps the second time series, output data is taken from the first time series up to the second time series's
starting date, the remainder of the data being taken from the second time series.
A different joining period can be specified by using the JPRD argument.
The two time series must have the same frequency.
TSJOIN(x = NULL, y = NULL, JPRD = NULL, ALLOWGAP = FALSE, WARN = FALSE, avoidCompliance = FALSE, ...)TSJOIN(x = NULL, y = NULL, JPRD = NULL, ALLOWGAP = FALSE, WARN = FALSE, avoidCompliance = FALSE, ...)
x |
First input time series that must satisfy the compliance control check defined in |
y |
Second input time series that must satisfy the compliance control check defined in |
JPRD |
This argument defines a joining period other than the starting period of the second time series.
It must be defined as |
ALLOWGAP |
if |
WARN |
Print a warning message if the two time series do not overlap or if the first time series starts after the |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a BIMETS time series that is built by joining the two input time series.
#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #TS ts1<-TSERIES((1:10),START=c(1985,1),FREQ=1) ts2<-TSERIES((1:10),START=c(2000,1),FREQ=1) TABIT(ts1,ts2,TSJOIN(ts1,ts2,ALLOWGAP=TRUE)) #XTS setBIMETSconf('BIMETS_CONF_CCT','XTS') n<-10 xArr<-(0:n) dateArr<-as.yearqtr('1997 Q1')+ 0:n/4 dataF<-data.frame(dateArr,xArr) ts1<-xts(dataF[,2],order.by=dataF[,1]) dateArr<-as.yearqtr('2000 Q1')+ 0:n/4 dataF<-data.frame(dateArr,xArr) ts2<-xts(dataF[,2],order.by=dataF[,1]) TABIT(ts1,ts2,TSJOIN(ts1,ts2,ALLOWGAP=TRUE,JPRD=yq2yp(as.yearqtr("2001 Q3")))) #restore default setBIMETSconf('BIMETS_CONF_CCT','TS')#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') #TS ts1<-TSERIES((1:10),START=c(1985,1),FREQ=1) ts2<-TSERIES((1:10),START=c(2000,1),FREQ=1) TABIT(ts1,ts2,TSJOIN(ts1,ts2,ALLOWGAP=TRUE)) #XTS setBIMETSconf('BIMETS_CONF_CCT','XTS') n<-10 xArr<-(0:n) dateArr<-as.yearqtr('1997 Q1')+ 0:n/4 dataF<-data.frame(dateArr,xArr) ts1<-xts(dataF[,2],order.by=dataF[,1]) dateArr<-as.yearqtr('2000 Q1')+ 0:n/4 dataF<-data.frame(dateArr,xArr) ts2<-xts(dataF[,2],order.by=dataF[,1]) TABIT(ts1,ts2,TSJOIN(ts1,ts2,ALLOWGAP=TRUE,JPRD=yq2yp(as.yearqtr("2001 Q3")))) #restore default setBIMETSconf('BIMETS_CONF_CCT','TS')
This function lags the input time series by the specified number of time periods.
TSLAG(x = NULL, L = 1, avoidCompliance = FALSE, verbose = FALSE, ...)TSLAG(x = NULL, L = 1, avoidCompliance = FALSE, verbose = FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
L |
Lag. Must be an integer, positive or negative. |
avoidCompliance |
If |
verbose |
If |
... |
Backward compatibility. |
This function returns a BIMETS time series built by lagging the input time series.
TSJOINTSEXTENDTSMERGEMOVAVGGETYEARPERIODTSLEAD
#DEFINE TS n<-10 ts1<-TSERIES(n:1,START=c(2000,1),FREQ=1) ts1[5]<-NA #print TSLAG TABIT(ts1,TSLAG(ts1,5)) n<-10 ts1<-TSERIES(n:1,START=c(2000,1),FREQ='D') ts1[5]<-NA #print TSLAG TABIT(ts1,TSLAG(ts1,5))#DEFINE TS n<-10 ts1<-TSERIES(n:1,START=c(2000,1),FREQ=1) ts1[5]<-NA #print TSLAG TABIT(ts1,TSLAG(ts1,5)) n<-10 ts1<-TSERIES(n:1,START=c(2000,1),FREQ='D') ts1[5]<-NA #print TSLAG TABIT(ts1,TSLAG(ts1,5))
This function leads the input time series by the specified number of time periods.
TSLEAD(x = NULL, L = 1, avoidCompliance = FALSE, verbose = FALSE, ...)TSLEAD(x = NULL, L = 1, avoidCompliance = FALSE, verbose = FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
L |
Lead. Must be an integer, positive or negative. |
avoidCompliance |
If |
verbose |
If |
... |
Backward compatibility. |
This function returns a BIMETS time series built by leading the input time series.
TSJOINTSEXTENDTSMERGEMOVAVGGETYEARPERIODTSLAG
#DEFINE TS n<-10 ts1<-TSERIES(n:1,START=c(2000,1),FREQ=1) ts1[5]<-NA #print TSLEAD TABIT(ts1,TSLEAD(ts1,5))#DEFINE TS n<-10 ts1<-TSERIES(n:1,START=c(2000,1),FREQ=1) ts1[5]<-NA #print TSLEAD TABIT(ts1,TSLEAD(ts1,5))
This function returns the time range and the frequency of an input time series.
TSLOOK(x=NULL, avoidCompliance=FALSE, ...)TSLOOK(x=NULL, avoidCompliance=FALSE, ...)
x |
Input time series that must satisfy the compliance control check defined in |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a list of numeric arrays built with the following elements:STARTY will contain the value of the starting yearSTARTP will contain the value of the starting periodENDY will contain the value of the ending yearENDP will contain the value of the ending periodFREQ will contain the value of the time series frequency
NOELSis.bimetsBIMETS indexingfromBIMETStoXTSfromBIMETStoTSGETYEARPERIODINTSTSINFO
#create series ts1<-TSERIES(INTS(1,10),START=c(2000,1),FREQ=12) ts1Look<-TSLOOK(ts1) print(ts1Look$STARTY) #print...2000 print(ts1Look$STARTP) #print...1 print(ts1Look$ENDY) #print...2000 print(ts1Look$ENDP) #print...10 print(ts1Look$FREQ) #print...12#create series ts1<-TSERIES(INTS(1,10),START=c(2000,1),FREQ=12) ts1Look<-TSLOOK(ts1) print(ts1Look$STARTY) #print...2000 print(ts1Look$STARTP) #print...1 print(ts1Look$ENDY) #print...2000 print(ts1Look$ENDP) #print...10 print(ts1Look$FREQ) #print...12
This function merges and concatenates two or more time series of the same frequency. The output time series will be defined over the union of dates for which the input time series are defined, from the earliest starting date to the latest ending date.
For each period, the output value will be set equal to the first non-missing value found in the input time series list by using the order of the arguments. If
all the input time series are missing at a period, then the output time series will be set to the missing value NA in the same period. Note that if the input time series' date spans do not intersect, TSMERGE(X1,X2,...,XN) returns a simple concatenation of X1, X2,..., XN.
By defining the argument fun, the value of the output time series can also be computed as a function of the values of the input time series in the same period (see example).
TSMERGE(..., fun = NULL, MV = FALSE, avoidCompliance = FALSE)TSMERGE(..., fun = NULL, MV = FALSE, avoidCompliance = FALSE)
... |
Input list of time series that must satisfy the compliance control check defined in |
fun |
By defining the argument |
MV |
If |
avoidCompliance |
If |
This function returns a BIMETS time series built by merging two or more input time series.
TSJOINTSEXTENDTSLAGTSPROJECTTSLEADTSTRIM
#DEFINE TS n<-10 ts1<-TSERIES(n:1,START=c(1995,1),FREQ=1) ts2<-TSERIES(n:1,START=c(2000,1),FREQ=1) ts2[5]<-NA ts1[10]<-NA #print TSMERGE TABIT(ts1,ts2,TSMERGE(ts1,ts2,fun='SUM',MV=TRUE)) #TS D n<-20 ts1<-TSERIES(n:1,START=c(1999,360),FREQ='D') ts2<-TSERIES(n:1,START=c(2000,1),FREQ='D') ts2[5]<-NA ts1[10]<-NA #print TSMERGE TABIT(ts1,ts2,TSMERGE(ts1,ts2,fun='SUM',MV=TRUE))#DEFINE TS n<-10 ts1<-TSERIES(n:1,START=c(1995,1),FREQ=1) ts2<-TSERIES(n:1,START=c(2000,1),FREQ=1) ts2[5]<-NA ts1[10]<-NA #print TSMERGE TABIT(ts1,ts2,TSMERGE(ts1,ts2,fun='SUM',MV=TRUE)) #TS D n<-20 ts1<-TSERIES(n:1,START=c(1999,360),FREQ='D') ts2<-TSERIES(n:1,START=c(2000,1),FREQ='D') ts2[5]<-NA ts1[10]<-NA #print TSMERGE TABIT(ts1,ts2,TSMERGE(ts1,ts2,fun='SUM',MV=TRUE))
This function projects the input time series into a time interval. The output class can be either a time series (default) or a one-dimensional array if the argument ARRAY=TRUE.
TSPROJECT(x=NULL, TSRANGE=NULL, ARRAY=FALSE, EXTEND=FALSE, avoidCompliance=FALSE,...)TSPROJECT(x=NULL, TSRANGE=NULL, ARRAY=FALSE, EXTEND=FALSE, avoidCompliance=FALSE,...)
x |
Input time series that must satisfy the compliance control check defined in |
TSRANGE |
Date range of data projection. |
ARRAY |
If |
EXTEND |
If |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns a BIMETS time series, or a numerical array if the argument ARRAY=TRUE, built by projecting the input time series into the provided TSRANGE.
TSJOINTSEXTENDTSMERGEMOVAVGGETYEARPERIODCUMSUMTSTRIM
#create yearly ts ts1<-TSERIES((1:10),START=c(2000,1),FREQ=1) print(TSPROJECT(ts1,TSRANGE=c(2002,1,2005,1))) #print projected ts from 2002 to 2005 print(TSPROJECT(ts1,TSRANGE=c(2001,1,2004,1),ARRAY=TRUE)) #print c(2,3,4,5) print(TSPROJECT(ts1,TSRANGE=c(1998,1,2002,1),EXTEND=TRUE,ARRAY=TRUE)) #print c(NA,NA,1,2,3)#create yearly ts ts1<-TSERIES((1:10),START=c(2000,1),FREQ=1) print(TSPROJECT(ts1,TSRANGE=c(2002,1,2005,1))) #print projected ts from 2002 to 2005 print(TSPROJECT(ts1,TSRANGE=c(2001,1,2004,1),ARRAY=TRUE)) #print c(2,3,4,5) print(TSPROJECT(ts1,TSRANGE=c(1998,1,2002,1),EXTEND=TRUE,ARRAY=TRUE)) #print c(NA,NA,1,2,3)
This function removes trailing or leading missing values NA from the input array or the input time series. Users can provide the value to be removed other than NA missing value by using the argument VALUE.
TSTRIM(x=NULL, VALUE=NA, TRAIL=TRUE, LEAD=TRUE, avoidCompliance=FALSE, ...)TSTRIM(x=NULL, VALUE=NA, TRAIL=TRUE, LEAD=TRUE, avoidCompliance=FALSE, ...)
x |
Input numerical array or time series that must satisfy the compliance control check defined in |
VALUE |
Target value to be removed. Default to missing value |
TRAIL |
If |
LEAD |
If |
avoidCompliance |
If |
... |
Backward compatibility. |
This function returns an object of the same class of the input, i.e. an array or a BIMETS time series, built by removing leading and trailing user-defined values.
TSLAGTSJOINTSMERGETSPROJECTCUMSUMINDEXNUM
#TS A n<-10 ts1<-TSERIES(c(NA,1:n,NA),START=c(2000,1),FREQ='A') TABIT(ts1,TSTRIM(ts1)) ts1<-TSERIES(c(NA,1:n,NA),START=c(2000,1),FREQ='A') TABIT(ts1,TSTRIM(ts1,TRAIL=FALSE)) ts1<-TSERIES(c(NA,1:n,NA),START=c(2000,1),FREQ='A') TABIT(ts1,TSTRIM(ts1,LEAD=FALSE)) ts1<-TSERIES(c(0,0,NA,1:n,NA,0),START=c(2000,1),FREQ='A') TABIT(ts1,TSTRIM(ts1,0))#TS A n<-10 ts1<-TSERIES(c(NA,1:n,NA),START=c(2000,1),FREQ='A') TABIT(ts1,TSTRIM(ts1)) ts1<-TSERIES(c(NA,1:n,NA),START=c(2000,1),FREQ='A') TABIT(ts1,TSTRIM(ts1,TRAIL=FALSE)) ts1<-TSERIES(c(NA,1:n,NA),START=c(2000,1),FREQ='A') TABIT(ts1,TSTRIM(ts1,LEAD=FALSE)) ts1<-TSERIES(c(0,0,NA,1:n,NA,0),START=c(2000,1),FREQ='A') TABIT(ts1,TSTRIM(ts1,0))
Given a time series list, this function returns list indices that refer to time serie having a magnitude greater than the user provided value. Magnitude M is defined as M = sqrt(sum(X_i^2)), given X_i the time series values. Missing values will be discarded with a warning message.
This function can be useful in comparing list of time series, e.g. differences between historical and simulated endogenous variables of an econometric model.
VERIFY_MAGNITUDE(x=list(), magnitude=10e-7, verbose=TRUE, ...)VERIFY_MAGNITUDE(x=list(), magnitude=10e-7, verbose=TRUE, ...)
x |
Input list, having elements as time series of class |
magnitude |
A positive number that is the maximum magnitude allowed. |
verbose |
If |
... |
Backward compatibility. |
This function returns the list indices related to time series that have a magnitude grater than the magnitude user argument.
TSJOINTSEXTENDTSMERGEMOVAVGGETYEARPERIODCUMSUM
#create ts ts1=TSERIES((1:10)*0.1, START=c(2000,1), FREQ=1) ts2=TSERIES((1:10)*0.01, START=c(2001,1), FREQ=4) ts3=TSERIES(c((1:10)*0.001,NA), START=c(2002,1), FREQ=12) myList=list(t1=ts1,t2=ts2,t3=ts3) print(VERIFY_MAGNITUDE(myList,magnitude=0.1))#create ts ts1=TSERIES((1:10)*0.1, START=c(2000,1), FREQ=1) ts2=TSERIES((1:10)*0.01, START=c(2001,1), FREQ=4) ts3=TSERIES(c((1:10)*0.001,NA), START=c(2002,1), FREQ=12) myList=list(t1=ts1,t2=ts2,t3=ts3) print(VERIFY_MAGNITUDE(myList,magnitude=0.1))
This function transforms an input variable of class yearmon() into an equivalent two-dimensional numerical array of type c(YEAR,PERIOD).
ym2yp(x = NULL)ym2yp(x = NULL)
x |
Input of class |
This function returns a two-dimensional numerical array of type c(YEAR,PERIOD).
#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') print(ym2yp(as.yearmon("Dec 2013"))); #print c(2013,12) print(ym2yp(c(as.yearmon('Jan 2000'),as.yearmon('Dec 1987'), as.yearmon('Jan 2003'),as.yearmon('Mar 2012'))))#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') print(ym2yp(as.yearmon("Dec 2013"))); #print c(2013,12) print(ym2yp(c(as.yearmon('Jan 2000'),as.yearmon('Dec 1987'), as.yearmon('Jan 2003'),as.yearmon('Mar 2012'))))
This function transforms an input variable of class yearqtr() into an equivalent two-dimensional numerical array of type c(YEAR,PERIOD).
yq2yp(x = NULL)yq2yp(x = NULL)
x |
Input of class |
This function returns a two-dimensional numerical array of type c(YEAR,PERIOD).
#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') print(yq2yp(as.yearqtr('2001 Q3'))); #print c(2001,3) print(yq2yp(c(as.yearqtr('2000 Q2'),as.yearqtr('1987 Q4'),as.yearqtr('2003 Q1'))))#day and month names can change depending on locale Sys.setlocale('LC_ALL','C') Sys.setlocale('LC_TIME','C') print(yq2yp(as.yearqtr('2001 Q3'))); #print c(2001,3) print(yq2yp(c(as.yearqtr('2000 Q2'),as.yearqtr('1987 Q4'),as.yearqtr('2003 Q1'))))