Package 'UComp' reference manual

Title:	Automatic Univariate Time Series Modelling of many Kinds
Description:	Comprehensive analysis and forecasting of univariate time series using automatic time series models of many kinds. Harvey AC (1989) <doi:10.1017/CBO9781107049994>. Pedregal DJ and Young PC (2002) <doi:10.1002/9780470996430>. Durbin J and Koopman SJ (2012) <doi:10.1093/acprof:oso/9780199641178.001.0001>. Hyndman RJ, Koehler AB, Ord JK, and Snyder RD (2008) <doi:10.1007/978-3-540-71918-2>. Gómez V, Maravall A (2000) <doi:10.1002/9781118032978>. Pedregal DJ, Trapero JR and Holgado E (2024) <doi:10.1016/j.ijforecast.2023.09.004>.
Authors:	Diego J. Pedregal [aut, cre]
Maintainer:	Diego J. Pedregal <[email protected]>
License:	GPL-3
Version:	5.0.4
Built:	2024-09-26 06:19:37 UTC
Source:	CRAN

Accuracy

Description

Accuracy for 1 time series y and several forecasting methods py and h steps ahead py is h x nMethods x nSeries

Usage

Accuracy(py, y, s = frequency(y), collectFun = mean)
Accuracy(py, y, s = frequency(y), collectFun = mean)

Arguments

`py`	matrix of forecasts (h x nMethods x nForecasts)
`y`	a matrix of actual values (n x nForecasts)
`s`	seasonal period, number of observations per year
`collectFun`	aggregation function (mean, median, etc.)

Value

Table of results

Author(s)

Diego J. Pedregal

Examples

## Not run: Accuracy(py, y, 12)
## Not run: Accuracy(py, y, 12)

acft

Description

Theoretical autocorrelation functions of ARMA models

Usage

acft(MApoly = 1, ARpoly = 1, ncoef = 38, s = 1)
acft(MApoly = 1, ARpoly = 1, ncoef = 38, s = 1)

Arguments

`MApoly`	coefficients of numerator polynomial in descending order
`ARpoly`	coefficients of denominator polynomial in descending order
`ncoef`	number of coefficients
`s`	seasonal period, number of observations per year

Value

Theoretical autocorrelation functions

Author(s)

Diego J. Pedregal

Examples

acft(c(1, -0.8), c(1, 0.8))
acft(c(1, -0.8), c(1, 0.8))

AIC.UComp

Description

Extract AIC value of UComp object

Usage

## S3 method for class 'UComp'
AIC(object, ..., k = 2)
## S3 method for class 'UComp'
AIC(object, ..., k = 2)

Arguments

`object`	Object of class “UComp”.
`...`	Additional inputs to function.
`k`	The penalty per parameter to be used.

Details

Selection criteria for models with different number of parameters, the smaller AIC the better. The formula used here is $AIC=-2 (ln(L) - k) / n$ , where $ln(L)$ is the log-likelihood at the optimum, $k$ is the number of parameters plus non-stationary states and $n$ is the number of observations. Mind that this formulation differs from the usual definition that does not divide by $n$ . This makes that AIC(m) and AIC(logLik(m)) give different results, being m an UComp object.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPassengers)
m1 <- UCmodel(y, model = "llt/equal/arma(0,0)")
AIC(m1)

## End(Not run)
## Not run: 
y <- log(AirPassengers)
m1 <- UCmodel(y, model = "llt/equal/arma(0,0)")
AIC(m1)

## End(Not run)

Airpassengers in Spain

Description

Foreign arrivals by air in Spain in thousands of passengers (airpas).

Usage

airpas
airpas

Format

Time series objects.

Monthly data from 1969

https://portal.mineco.gob.es/es-es/economiayempresa/EconomiaInformesMacro/Paginas/bdsice.aspx

Examples

## Not run: 
 airpas

## End(Not run)
## Not run: 
 airpas

## End(Not run)

ARIMA

Description

Runs all relevant functions for ARIMA modelling

Usage

ARIMA(
  y,
  u = NULL,
  model = NULL,
  cnst = NULL,
  s = frequency(y),
  criterion = "bic",
  h = 2 * s,
  verbose = FALSE,
  lambda = 1,
  maxOrders = c(3, 2, 3, 2, 1, 2),
  bootstrap = FALSE,
  nSimul = 5000,
  fast = FALSE
)
ARIMA(
  y,
  u = NULL,
  model = NULL,
  cnst = NULL,
  s = frequency(y),
  criterion = "bic",
  h = 2 * s,
  verbose = FALSE,
  lambda = 1,
  maxOrders = c(3, 2, 3, 2, 1, 2),
  bootstrap = FALSE,
  nSimul = 5000,
  fast = FALSE
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. A vector c(p,d,q,P,D,Q) containing the model orders of an ARIMA(p,d,q)x(P,D,Q)_s model. A constant may be estimated with the cnst input. Use a NULL to automatically identify the ARIMA model.
`cnst`	flag to include a constant in the model (TRUE/FALSE/NULL). Use NULL to estimate
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`criterion`	information criterion for identification stage ("aic", "bic", "aicc")
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`verbose`	intermediate estimation output (TRUE / FALSE)
`lambda`	Box-Cox lambda parameter (NULL: estimate)
`maxOrders`	a vector c(p,d,q,P,D,Q) containing the maximum orders of model orders to search for in the automatic identification
`bootstrap`	use bootstrap simulation for predictive distributions
`nSimul`	number of simulation runs for bootstrap simulation of predictive distributions
`fast`	fast identification (avoids post-identification checks)

Details

See help of ARIMAmodel.

Value

An object of class ARIMA. See ARIMAmodel.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPAssengers)
m1 <- ARIMA(y)
m1 <- ARIMA(y, lambda = NULL)

## End(Not run)
## Not run: 
y <- log(AirPAssengers)
m1 <- ARIMA(y)
m1 <- ARIMA(y, lambda = NULL)

## End(Not run)

ARIMAestim

Description

Estimates and forecasts ARIMA models

Usage

ARIMAestim(m)
ARIMAestim(m)

Arguments

`m`	an object of type `ARIMA` created with `ARIMAmodel`

Details

ARIMAestim estimates and forecasts a time series using an ARIMA model

Value

The same input object with the appropriate fields filled in, in particular:

`p`	Estimated parameters
`yFor`	Forecasted values of output
`yForV`	Variance of forecasted values of output
`ySimul`	Bootstrap simulations for forecasting distribution evaluation

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ARIMAsetup(log(gdp))
m1 <- ARIMAestim(m1)

## End(Not run)
## Not run: 
m1 <- ARIMAsetup(log(gdp))
m1 <- ARIMAestim(m1)

## End(Not run)

ARIMAmodel

Description

Estimates and forecasts ARIMA general univariate models

Usage

ARIMAmodel(
  y,
  u = NULL,
  model = NULL,
  cnst = NULL,
  s = frequency(y),
  criterion = "bic",
  h = 2 * s,
  verbose = FALSE,
  lambda = 1,
  maxOrders = c(3, 2, 3, 2, 1, 2),
  bootstrap = FALSE,
  nSimul = 5000,
  fast = FALSE
)
ARIMAmodel(
  y,
  u = NULL,
  model = NULL,
  cnst = NULL,
  s = frequency(y),
  criterion = "bic",
  h = 2 * s,
  verbose = FALSE,
  lambda = 1,
  maxOrders = c(3, 2, 3, 2, 1, 2),
  bootstrap = FALSE,
  nSimul = 5000,
  fast = FALSE
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. A vector c(p,d,q,P,D,Q) containing the model orders of an ARIMA(p,d,q)x(P,D,Q)_s model. A constant may be estimated with the cnst input. Use a NULL to automatically identify the ARIMA model.
`cnst`	flag to include a constant in the model (TRUE/FALSE/NULL). Use NULL to estimate
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`criterion`	information criterion for identification stage ("aic", "bic", "aicc")
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`verbose`	intermediate estimation output (TRUE / FALSE)
`lambda`	Box-Cox lambda parameter (NULL: estimate)
`maxOrders`	a vector c(p,d,q,P,D,Q) containing the maximum orders of model orders to search for in the automatic identification
`bootstrap`	use bootstrap simulation for predictive distributions
`nSimul`	number of simulation runs for bootstrap simulation of predictive distributions
`fast`	fast identification (avoids post-identification checks)

Details

ARIMAmodel is a function for modelling and forecasting univariate time series with Autoregressive Integrated Moving Average (ARIMA) time series models. It sets up the model with a number of control variables that govern the way the rest of functions in the package will work. It also estimates the model parameters by Maximum Likelihood and forecasts the data.

Value

An object of class ARIMA. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any ARIMA object as specified in what follows (function ARIMA fills in all of them at once):

After running ARIMAmodel or ARIMA:

`p`	Estimated parameters
`yFor`	Forecasted values of output
`yForV`	Variance of forecasted values of output
`ySimul`	Bootstrap simulations for forecasting distribution evaluation

After running ARIMAvalidate:

table

Estimation and validation table

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPAssengers)
m1 <- ARIMAmodel(y)
m1 <- ARIMAmodel(y, lambda = NULL)

## End(Not run)
## Not run: 
y <- log(AirPAssengers)
m1 <- ARIMAmodel(y)
m1 <- ARIMAmodel(y, lambda = NULL)

## End(Not run)

ARIMAsetup

Description

Sets up ARIMA general models

Usage

ARIMAsetup(
  y,
  u = NULL,
  model = NULL,
  cnst = NULL,
  s = frequency(y),
  criterion = "bic",
  h = 2 * s,
  verbose = FALSE,
  lambda = 1,
  maxOrders = c(3, 2, 3, 2, 1, 2),
  bootstrap = FALSE,
  nSimul = 5000,
  fast = FALSE
)
ARIMAsetup(
  y,
  u = NULL,
  model = NULL,
  cnst = NULL,
  s = frequency(y),
  criterion = "bic",
  h = 2 * s,
  verbose = FALSE,
  lambda = 1,
  maxOrders = c(3, 2, 3, 2, 1, 2),
  bootstrap = FALSE,
  nSimul = 5000,
  fast = FALSE
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. A vector c(p,d,q,P,D,Q) containing the model orders of an ARIMA(p,d,q)x(P,D,Q)_s model. A constant may be estimated with the cnst input. Use a NULL to automatically identify the ARIMA model.
`cnst`	flag to include a constant in the model (TRUE/FALSE/NULL). Use NULL to estimate
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`criterion`	information criterion for identification stage ("aic", "bic", "aicc")
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`verbose`	intermediate estimation output (TRUE / FALSE)
`lambda`	Box-Cox lambda parameter (NULL: estimate)
`maxOrders`	a vector c(p,d,q,P,D,Q) containing the maximum orders of model orders to search for in the automatic identification
`bootstrap`	use bootstrap simulation for predictive distributions
`nSimul`	number of simulation runs for bootstrap simulation of predictive distributions
`fast`	fast identification (avoids post-identification checks)

Details

See help of ARIMAmodel.

Value

An object of class ARIMA. See ARIMAmodel.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPAssengers)
m1 <- ARIMAsetup(y)
m1 <- ARIMAsetup(y, lambda = NULL)

## End(Not run)
## Not run: 
y <- log(AirPAssengers)
m1 <- ARIMAsetup(y)
m1 <- ARIMAsetup(y, lambda = NULL)

## End(Not run)

ARIMAvalidate

Description

Shows a table of estimation and diagnostics results for ARIMA models

Usage

ARIMAvalidate(m)
ARIMAvalidate(m)

Arguments

`m`	an object of type `ARIMA` created with `ARIMAmodel`

Value

The same input object with the appropriate fields filled in, in particular:

table

Estimation and validation table

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ARIMAmodel(log(gdp))
m1 <- ARIMAvalidate(m1)

## End(Not run)
## Not run: 
m1 <- ARIMAmodel(log(gdp))
m1 <- ARIMAvalidate(m1)

## End(Not run)

arma2tsi

Description

AR polynomial coefficients of ARMA model

Usage

arma2tsi(MApoly, ARpoly, n = 100)
arma2tsi(MApoly, ARpoly, n = 100)

Arguments

`MApoly`	coefficients of numerator polynomial in descending order
`ARpoly`	coefficients of denominator polynomial in descending order
`n`	number of coefficients

Author(s)

Diego J. Pedregal

armaFilter

Description

Filter of time series

Usage

armaFilter(MA = 1, AR = 1, y)
armaFilter(MA = 1, AR = 1, y)

Arguments

`MA`	numerator polynomial
`AR`	denominator polynomial
`y`	a vector, ts or tsibble object

Value

Filtered time series

Author(s)

Diego J. Pedregal

Examples

y <- armaFilter(1, c(1 , -0.8), rnorm(200))
y <- armaFilter(1, c(1 , -0.8), rnorm(200))

auxInvBoxCox

Description

Inverse of Box-Cox transformation

Usage

auxInvBoxCox(y, lambda)
auxInvBoxCox(y, lambda)

Arguments

`y`	matrix, array or vector
`lambda`	lambda parameter of Box-Cox transformation

Author(s)

Diego J. Pedregal

BIC.UComp

Description

Extract BIC (or SBC) value of UComp object

Usage

## S3 method for class 'UComp'
BIC(object, ...)
## S3 method for class 'UComp'
BIC(object, ...)

Arguments

`object`	Object of class “UComp”.
`...`	Additional inputs to function.

Details

Selection criteria for models with different number of parameters, the smaller BIC the better. The formula used here is $BIC=(-2 ln(L) + k ln(n)) / n$ , where $ln(L)$ is the log-likelihood at the optimum, $k$ is the number of parameters plus non-stationary states and $n$ is the number of observations. Mind that this formulation differs from the usual definition that does not divide by $n$ . This makes that BIC(m) and BIC(logLik(m)) give different results, being m an UComp object.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPassengers)
m1 <- UCmodel(y, model = "llt/equal/arma(0,0)")
BIC(m1)

## End(Not run)
## Not run: 
y <- log(AirPassengers)
m1 <- UCmodel(y, model = "llt/equal/arma(0,0)")
BIC(m1)

## End(Not run)

box.cox

Description

Runs Box-Cox transform of a time series

Usage

box.cox(x, lambda)
box.cox(x, lambda)

Arguments

`x`	Time series object.
`lambda`	Lambda parameter for Box-Cox transform.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- box.cox(AirPassengers, 0.5)
plot(y)

## End(Not run)
## Not run: 
y <- box.cox(AirPassengers, 0.5)
plot(y)

## End(Not run)

Methane concentration at Cape Grim in Australia

Description

Methane concentration at Cape Grim in Australia (ch4).

Usage

ch4
ch4

Format

Time series objects.

Monthly data from January 1992 to December 2019

Source

CH4 data

Examples

## Not run: 
 ch4

## End(Not run)
## Not run: 
 ch4

## End(Not run)

colMedians

Description

Medians of matrix by columns

Usage

colMedians(x, na.rm = TRUE, ...)
colMedians(x, na.rm = TRUE, ...)

Arguments

`x`	a matrix
`na.rm`	boolean indicating whether to remove nans
`...`	rest of inputs

Value

A vector with all the medians

Author(s)

Diego J. Pedregal

Examples

s <- colMedians(matrix(4, 3, 2))
s <- colMedians(matrix(4, 3, 2))

conv

Description

1D convolution: filtering or polynomial multiplication

Usage

conv(...)
conv(...)

Arguments

...

list of vectors to convolute

Value

Convolution of all input vectors

Author(s)

Diego J. Pedregal

Examples

conv(c(1, -1), c(1, -2, 1))
conv(c(1, -1), c(1, 0.8))
conv(c(1, -1), c(1, -2, 1))
conv(c(1, -1), c(1, 0.8))

cusum

Description

Cusum and cusumsq tests

Usage

cusum(y, runFromTest = FALSE)
cusum(y, runFromTest = FALSE)

Arguments

`y`	a vector, ts or tsibble object
`runFromTest`	internal check variable

Author(s)

Diego J. Pedregal

Examples

cusum(AirPassengers)
cusum(AirPassengers)

dif

Description

Discrete differencing of time series

Usage

dif(y, difs = 1, seas = 1)
dif(y, difs = 1, seas = 1)

Arguments

`y`	a vector, ts or tsibble object
`difs`	vector with differencing orders
`seas`	vector of seasonal periods

Value

Differenced time series

Author(s)

Diego J. Pedregal

Examples

dif(AirPassengers)
dif(AirPassengers, 2)
dif(AirPassengers, c(1, 1), c(1, 12))
dif(AirPassengers)
dif(AirPassengers, 2)
dif(AirPassengers, c(1, 1), c(1, 12))

ETS

Description

Runs all relevant functions for ETS modelling

Usage

ETS(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  identAll = FALSE,
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(1e-08, 1 - 1e-08),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999
)
ETS(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  identAll = FALSE,
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(1e-08, 1 - 1e-08),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component with one or two letters: Error: ? / A / M Trend: ? / N / A / Ad / M / Md Seasonal: ? / N / A / M
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`lambda`	Box-Cox lambda parameter (NULL: estimate)
`armaIdent`	check for arma models for error component (TRUE / FALSE).
`identAll`	run all models to identify the best one (TRUE / FALSE)
`forIntervals`	estimate forecasting intervals (TRUE / FALSE)
`bootstrap`	use bootstrap simulation for predictive distributions
`nSimul`	number of simulation runs for bootstrap simulation of predictive distributions
`verbose`	intermediate estimation output (TRUE / FALSE)
`alphaL`	constraints limits for alpha parameter
`betaL`	constraints limits for beta parameter
`gammaL`	constraints limits for gamma parameter
`phiL`	constraints limits for phi parameter
`p0`	initial values for parameter search (alpha, beta, phi, gamma) with consraints: 0 < alpha < 1 0 < beta < alpha 0 < phi < 1 0 < gamma < 1 - alpha

Details

See help of ETSmodel.

Value

An object of class ETS. See ETSmodel.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPAssengers)
m1 <- ETS(y)
m1 <- ETS(y, model = "MAM")

## End(Not run)
## Not run: 
y <- log(AirPAssengers)
m1 <- ETS(y)
m1 <- ETS(y, model = "MAM")

## End(Not run)

ETScomponents

Description

Estimates components of ETS models

Usage

ETScomponents(m)
ETScomponents(m)

Arguments

`m`	an object of type `ETS` created with `ETSmodel`

Value

The same input object with the appropriate fields filled in, in particular:

comp

Estimated components in matrix form

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ETS(log(gdp))
m1 <- ETScomponents(m1)

## End(Not run)
## Not run: 
m1 <- ETS(log(gdp))
m1 <- ETScomponents(m1)

## End(Not run)

ETSestim

Description

Estimates and forecasts ETS models

Usage

ETSestim(m)
ETSestim(m)

Arguments

`m`	an object of type `ETS` created with `ETSmodel`

Details

ETSestim estimates and forecasts a time series using an an ETS model

Value

The same input object with the appropriate fields filled in, in particular:

`p`	Estimated parameters
`yFor`	Forecasted values of output
`yForV`	Variance of forecasted values of output
`ySimul`	Bootstrap simulations for forecasting distribution evaluation

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ETSsetup(log(gdp))
m1 <- ETSestim(m1)

## End(Not run)
## Not run: 
m1 <- ETSsetup(log(gdp))
m1 <- ETSestim(m1)

## End(Not run)

ETSmodel

Description

Estimates and forecasts ETS general univariate models

Usage

ETSmodel(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = max(2 * s, 6),
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  identAll = FALSE,
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(1e-08, 1 - 1e-08),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999
)
ETSmodel(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = max(2 * s, 6),
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  identAll = FALSE,
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(1e-08, 1 - 1e-08),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component with one or two letters: Error: ? / A / M Trend: ? / N / A / Ad / M / Md Seasonal: ? / N / A / M
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`lambda`	Box-Cox lambda parameter (NULL: estimate)
`armaIdent`	check for arma models for error component (TRUE / FALSE).
`identAll`	run all models to identify the best one (TRUE / FALSE)
`forIntervals`	estimate forecasting intervals (TRUE / FALSE)
`bootstrap`	use bootstrap simulation for predictive distributions
`nSimul`	number of simulation runs for bootstrap simulation of predictive distributions
`verbose`	intermediate estimation output (TRUE / FALSE)
`alphaL`	constraints limits for alpha parameter
`betaL`	constraints limits for beta parameter
`gammaL`	constraints limits for gamma parameter
`phiL`	constraints limits for phi parameter
`p0`	initial values for parameter search (alpha, beta, phi, gamma) with consraints: 0 < alpha < 1 0 < beta < alpha 0 < phi < 1 0 < gamma < 1 - alpha

Details

ETSmodel is a function for modelling and forecasting univariate time series with ExponenTial Smoothing (ETS) time series models. It sets up the model with a number of control variables that govern the way the rest of functions in the package will work. It also estimates the model parameters by Maximum Likelihood and forecasts the data.

Value

An object of class ETS. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any ETS object as specified in what follows (function ETS fills in all of them at once):

After running ETSmodel or ETSestim:

`p`	Estimated parameters
`criteria`	Values for estimation criteria (LogLik, AIC, BIC, AICc)
`yFor`	Forecasted values of output
`yForV`	Variance of forecasted values of output
`ySimul`	Bootstrap simulations for forecasting distribution evaluation

After running ETSvalidate:

`table`	Estimation and validation table
`comp`	Estimated components in matrix form

After running ETScomponents:

comp

Estimated components in matrix form

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPAssengers)
m1 <- ETSmodel(y)
m1 <- ETSmodel(y, model = "A?A")

## End(Not run)
## Not run: 
y <- log(AirPAssengers)
m1 <- ETSmodel(y)
m1 <- ETSmodel(y, model = "A?A")

## End(Not run)

ETSsetup

Description

Sets up ETS general univariate models

Usage

ETSsetup(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  identAll = FALSE,
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(1e-08, 1 - 1e-08),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999
)
ETSsetup(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  identAll = FALSE,
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(1e-08, 1 - 1e-08),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component with one or two letters: Error: ? / A / M Trend: ? / N / A / Ad / M / Md Seasonal: ? / N / A / M
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`lambda`	Box-Cox lambda parameter (NULL: estimate)
`armaIdent`	check for arma models for error component (TRUE / FALSE).
`identAll`	run all models to identify the best one (TRUE / FALSE)
`forIntervals`	estimate forecasting intervals (TRUE / FALSE)
`bootstrap`	use bootstrap simulation for predictive distributions
`nSimul`	number of simulation runs for bootstrap simulation of predictive distributions
`verbose`	intermediate estimation output (TRUE / FALSE)
`alphaL`	constraints limits for alpha parameter
`betaL`	constraints limits for beta parameter
`gammaL`	constraints limits for gamma parameter
`phiL`	constraints limits for phi parameter
`p0`	initial values for parameter search (alpha, beta, phi, gamma) with consraints: 0 < alpha < 1 0 < beta < alpha 0 < phi < 1 0 < gamma < 1 - alpha

Details

See help of ETSmodel.

Value

An object of class ETS. See ETSmodel.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPAssengers)
m1 <- ETSsetup(y)
m1 <- ETSsetup(y,  model = "???")
m1 <- ETSsetup(y,  model = "?AA")

## End(Not run)
## Not run: 
y <- log(AirPAssengers)
m1 <- ETSsetup(y)
m1 <- ETSsetup(y,  model = "???")
m1 <- ETSsetup(y,  model = "?AA")

## End(Not run)

ETSvalidate

Description

Shows a table of estimation and diagnostics results for ETS models

Usage

ETSvalidate(m)
ETSvalidate(m)

Arguments

`m`	an object of type `ETS` created with `ETSmodel`

Value

The same input object with the appropriate fields filled in, in particular:

table

Estimation and validation table

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ETSmodel(log(gdp))
m1 <- ETSvalidate(m1)

## End(Not run)
## Not run: 
m1 <- ETSmodel(log(gdp))
m1 <- ETSvalidate(m1)

## End(Not run)

extract

Description

Reorder data frame returning column col reordered according to the values in column accordingTo

Usage

extract(x, col, accordingTo = 1)
extract(x, col, accordingTo = 1)

Arguments

`x`	a data frame
`col`	column to be ordered
`accordingTo`	column to take as the pattern

Value

data frame reordered

Author(s)

Diego J. Pedregal

fitted.ETS

Description

Fitted output values of ETS object

Fitted output values of PTS object

Fitted output values of TETS object

Usage

## S3 method for class 'ETS'
fitted(object, ...)

## S3 method for class 'PTS'
fitted(object, ...)

## S3 method for class 'TETS'
fitted(object, ...)
## S3 method for class 'ETS'
fitted(object, ...)

## S3 method for class 'PTS'
fitted(object, ...)

## S3 method for class 'TETS'
fitted(object, ...)

Arguments

`object`	Object of class “TETS”.
`...`	Additional inputs to function.

Details

See help of ETS.

See help of PTS.

See help of TETS.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ETSmodel(log(gdp))
fitted(m1)

## End(Not run)
## Not run: 
m1 <- PTSmodel(log(AirPassengers))
fitted(m1)

## End(Not run)
## Not run: 
m1 <- TETSmodel(log(gdp))
fitted(m1)

## End(Not run)
## Not run: 
m1 <- ETSmodel(log(gdp))
fitted(m1)

## End(Not run)
## Not run: 
m1 <- PTSmodel(log(AirPassengers))
fitted(m1)

## End(Not run)
## Not run: 
m1 <- TETSmodel(log(gdp))
fitted(m1)

## End(Not run)

gaussTest

Description

Gaussianity tests

Usage

gaussTest(y, runFromTests = FALSE)
gaussTest(y, runFromTests = FALSE)

Arguments

`y`	a vector, ts or tsibble object
`runFromTests`	internal check

Author(s)

Diego J. Pedregal

Examples

gaussTest(AirPassengers)
gaussTest(AirPassengers)

Spanish GDP

Description

Quarterly real Spanish Gross Domestic Product (gdp)

Usage

gdp
gdp

Format

Time series objects.

Quarterly since 1995

https://portal.mineco.gob.es/es-es/economiayempresa/EconomiaInformesMacro/Paginas/bdsice.aspx

Examples

## Not run: 
 gdp

## End(Not run)
## Not run: 
 gdp

## End(Not run)

getp0

Description

Get initial conditions for parameters of UComp object

Usage

getp0(y, model = "llt/equal/arma(0,0)", periods = NA)
getp0(y, model = "llt/equal/arma(0,0)", periods = NA)

Arguments

`y`	a time series to forecast.
`model`	any valid `UComp` model without any ?.
`periods`	vector of fundamental period and harmonics required.

Details

Provides initial parameters of a given model for the time series. They may be changed arbitrarily by the user to include as an input p0 to UC or UCmodel functions (see example below). There is no guarantee that the model will converge and selecting initial conditions should be used with care.

Value

A set of parameters p0 of an object of class UComp to use as input to UC, UCmodel or UCsetup.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
p0 <- getp0(log(AirPassengers), model = "llt/equal/arma(0,0)")
p0[1] <- 0  # p0[1] <- NA
m <- UCmodel(log(AirPassengers), model = "llt/equal/arma(0,0)", p0 = p0)

## End(Not run)
## Not run: 
p0 <- getp0(log(AirPassengers), model = "llt/equal/arma(0,0)")
p0[1] <- 0  # p0[1] <- NA
m <- UCmodel(log(AirPassengers), model = "llt/equal/arma(0,0)", p0 = p0)

## End(Not run)

ident

Description

Autocorrelation functions of a time series

Usage

ident(y, nCoef = min(37, floor(length(y)/4)), nPar = 0, runFromTests = FALSE)
ident(y, nCoef = min(37, floor(length(y)/4)), nPar = 0, runFromTests = FALSE)

Arguments

`y`	a vector, ts or tsibble object
`nCoef`	number of autocorrelation coefficients to estimate
`nPar`	number of parameters in a model if y is a residual
`runFromTests`	internal check

Value

A vector with all the dimensions

Author(s)

Diego J. Pedregal

Examples

ident(AirPassengers)
ident(AirPassengers)

inv.box.cox

Description

Runs inverse of Box-Cox transform of a time series

Usage

inv.box.cox(x, lambda)
inv.box.cox(x, lambda)

Arguments

`x`	Transformed time series object.
`lambda`	Lambda parameter used for Box-Cox transform.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- inv.box.cox(box.cox(AirPassengers, 0.5), 0.5)
plot(y)

## End(Not run)
## Not run: 
y <- inv.box.cox(box.cox(AirPassengers, 0.5), 0.5)
plot(y)

## End(Not run)

invBoxCox

Description

Calculates inverse of Box-Cox transformation with confidence bands, calculated as const time the standard error

Usage

invBoxCox(y, yVar, lambda, const = 2)
invBoxCox(y, yVar, lambda, const = 2)

Arguments

`y`	matrix, array or vector
`yVar`	matrix, array or vector of variances of y
`lambda`	lambda parameter of Box-Cox transformation
`const`	number of standard error for confidence band

Author(s)

Diego J. Pedregal

Spanish Industrial Production Index

Description

Spanish Industrial Production Index (ipi).

Usage

ipi
ipi

Format

Objeto time series.

Monthly since 1975

https://portal.mineco.gob.es/es-es/economiayempresa/EconomiaInformesMacro/Paginas/bdsice.aspx

Examples

## Not run: 
 ipi

## End(Not run)
## Not run: 
 ipi

## End(Not run)

modelUC2arma

Description

Extracts arma part of modelUC model

Usage

modelUC2arma(model)
modelUC2arma(model)

Arguments

model

a UC model

Value

arma orders

Author(s)

Diego J. Pedregal

modelUC2PTS

Description

Translates modelUC to model PTS

Usage

modelUC2PTS(modelUC)
modelUC2PTS(modelUC)

Arguments

modelUC

a UC model

Value

a PTS model

Author(s)

Diego J. Pedregal

OECD GDP

Description

Seasonally adjusted quarterly OECD real gross domestic product (OECDgdp).

Usage

OECDgdp
OECDgdp

Format

Time series objects.

Quarterly data from 1962 to 2019

https://portal.mineco.gob.es/es-es/economiayempresa/EconomiaInformesMacro/Paginas/bdsice.aspx

Examples

## Not run: 
 OECDgdp

## End(Not run)
## Not run: 
 OECDgdp

## End(Not run)

plot.ARIMA

Description

Plot zplane of ARIMA object

Usage

## S3 method for class 'ARIMA'
plot(x, ...)
## S3 method for class 'ARIMA'
plot(x, ...)

Arguments

`x`	Object of class “ARIMA”.
`...`	Additional inputs to function.

Details

See help of ARIMA.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ARIMAmodel(log(gdp))
plot(m1)

## End(Not run)
## Not run: 
m1 <- ARIMAmodel(log(gdp))
plot(m1)

## End(Not run)

plot.ETS

Description

Plot components of ETS object

Plot components of PTS object

Plot components of TETS object

Usage

## S3 method for class 'ETS'
plot(x, ...)

## S3 method for class 'PTS'
plot(x, ...)

## S3 method for class 'TETS'
plot(x, ...)
## S3 method for class 'ETS'
plot(x, ...)

## S3 method for class 'PTS'
plot(x, ...)

## S3 method for class 'TETS'
plot(x, ...)

Arguments

`x`	Object of class “TETS”.
`...`	Additional inputs to function.

Details

See help of ETS.

See help of PTS.

See help of TETS.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ETSmodel(log(gdp))
plot(m1)

## End(Not run)
## Not run: 
m1 <- PTS(log(AirPassengers))
plot(m1)

## End(Not run)
## Not run: 
m1 <- TETSmodel(log(gdp))
plot(m1)

## End(Not run)
## Not run: 
m1 <- ETSmodel(log(gdp))
plot(m1)

## End(Not run)
## Not run: 
m1 <- PTS(log(AirPassengers))
plot(m1)

## End(Not run)
## Not run: 
m1 <- TETSmodel(log(gdp))
plot(m1)

## End(Not run)

plotAcfPacf

Description

Plot of ACF and PACF

Usage

plotAcfPacf(ACF, PACF, s = 1, n = NA, runFromTest = FALSE)
plotAcfPacf(ACF, PACF, s = 1, n = NA, runFromTest = FALSE)

Arguments

`ACF`	variable to plot
`PACF`	second variable to plot
`s`	seasonal period
`n`	number of coefficients
`runFromTest`	internal check variable

Author(s)

Diego J. Pedregal

plotBar

Description

Plot variable in bars

Usage

plotBar(ACF, s = 1, n = NA, label = "ACF")
plotBar(ACF, s = 1, n = NA, label = "ACF")

Arguments

`ACF`	variable to plot
`s`	seasonal period
`n`	number of coefficients
`label`	label for plot

Value

Handle of plot

Author(s)

Diego J. Pedregal

plotSlide

Description

Plot summarised results from slide

Usage

plotSlide(py1, y, orig, step = 1, errorFun, collectFun = mean)
plotSlide(py1, y, orig, step = 1, errorFun, collectFun = mean)

Arguments

`py1`	output from slide function
`y`	a vector or matrix of time series (the same used in slide call)
`orig`	starting forecasting origin (the same used in slide call)
`step`	observations ahead to move the forecasting origin (the same used in slide call)
`errorFun`	user function to calculate error measures
`collectFun`	aggregation function (mean, median, etc.)

Value

Results

Author(s)

Diego J. Pedregal

Examples

## Not run: plotSlide(py1, AirPassengers, 100, 1, errorFun)
## Not run: plotSlide(py1, AirPassengers, 100, 1, errorFun)

plus_one

Description

Returns date of next to end time series y

Usage

plus_one(y)
plus_one(y)

Arguments

`y`	a ts object

Value

Next time stamp

Author(s)

Diego J. Pedregal

predict.UComp

Description

Forecasting using structural Unobseved Components models with prediction intervals

Usage

## S3 method for class 'UComp'
predict(object, newdata = NULL, n.ahead = NULL, level = 0.95, ...)
## S3 method for class 'UComp'
predict(object, newdata = NULL, n.ahead = NULL, level = 0.95, ...)

Arguments

`object`	Object of class “UComp”.
`newdata`	New output data to apply “UComp” object to.
`n.ahead`	Number of steps ahead to forecast or new inputs variables including their predictions.
`level`	Confidence level for prediction intervals.
`...`	Ignored.

Details

See help of UC.

Value

A matrix with the mean forecasts and lower and upper prediction intervals

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPassengers)
m1 <- UCmodel(y, model = "llt/eq/arma(0,0)")
f1 <- predict(m1)

## End(Not run)
## Not run: 
y <- log(AirPassengers)
m1 <- UCmodel(y, model = "llt/eq/arma(0,0)")
f1 <- predict(m1)

## End(Not run)

print.ARIMA

Description

Prints an ARIMA object

Prints an ETS object

Prints a PTS object

Prints a TOBIT TETS object

Usage

## S3 method for class 'ARIMA'
print(x, ...)

## S3 method for class 'ETS'
print(x, ...)

## S3 method for class 'PTS'
print(x, ...)

## S3 method for class 'TETS'
print(x, ...)
## S3 method for class 'ARIMA'
print(x, ...)

## S3 method for class 'ETS'
print(x, ...)

## S3 method for class 'PTS'
print(x, ...)

## S3 method for class 'TETS'
print(x, ...)

Arguments

`x`	Object of class “TETS”.
`...`	Additional inputs to handle the way to print output.

Details

See help of ARIMA.

See help of ETS.

See help of PTS.

See help of TETS.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ARIMAmodel(log(gdp))
print(m1)

## End(Not run)
## Not run: 
m1 <- ETSmodel(log(gdp))
print(m1)

## End(Not run)
## Not run: 
m1 <- PTSmodel(log(AirPassengers))
print(m1)

## End(Not run)
## Not run: 
m1 <- TETSmodel(log(gdp))
print(m1)

## End(Not run)
## Not run: 
m1 <- ARIMAmodel(log(gdp))
print(m1)

## End(Not run)
## Not run: 
m1 <- ETSmodel(log(gdp))
print(m1)

## End(Not run)
## Not run: 
m1 <- PTSmodel(log(AirPassengers))
print(m1)

## End(Not run)
## Not run: 
m1 <- TETSmodel(log(gdp))
print(m1)

## End(Not run)

PTS

Description

Estimates, forecasts and smooth PTS general univariate models

Usage

PTS(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  verbose = FALSE
)
PTS(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  verbose = FALSE
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component with one or two letters: Error: ? / N / A Trend: ? / N / A / Ad / L Seasonal: ? / N / A / D (trigonometric with different variances)
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`lambda`	Box-Cox lambda parameter (NULL: estimate)
`armaIdent`	check for arma models for error component (TRUE / FALSE).
`verbose`	intermediate estimation output (TRUE / FALSE)

Details

PTS is a function for modelling and forecasting univariate time series according to Power-Trend-Seasonal (PTS). It sets up the model with a number of control variables that govern the way the rest of functions in the package work. It also estimates the model parameters by Maximum Likelihood and forecasts the data. Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Value

An object of class PTS. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any PTS object as specified in what follows (function PTS fills in all of them at once):

After running PTSmodel or PTSestim:

p0: Initial values for parameter search
p: Estimated parameters
lambda: Estimated Box-Cox lambda parameter
v: Estimated innovations (white noise in correctly specified models)
yFor: Forecasted values of output
yForV: Variance of forecasted values of output

After running PTSvalidate:

table: Estimation and validation table

After running PTScomponents:

comp: Estimated components in matrix form

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- PTS(log(AirPassengers))

## End(Not run)
## Not run: 
m1 <- PTS(log(AirPassengers))

## End(Not run)

PTS2modelUC

Description

Translates PTS model to UC model

Usage

PTS2modelUC(model, armaOrders = c(0, 0))
PTS2modelUC(model, armaOrders = c(0, 0))

Arguments

`model`	a PTS model
`armaOrders`	arma orders of noise model

Value

a UC model

Author(s)

Diego J. Pedregal

PTScomponents

Description

Estimates components of PTS models

Usage

PTScomponents(m)
PTScomponents(m)

Arguments

`m`	an object of type `PTS` created with `PTSmodel`

Value

The same input object with the appropriate fields filled in, in particular:

comp: Estimated components in matrix form

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- PTS(log(AirPassengers))
m1 <- PTScomponents(m1)

## End(Not run)
## Not run: 
m1 <- PTS(log(AirPassengers))
m1 <- PTScomponents(m1)

## End(Not run)

PTSestim

Description

Estimates and forecasts PTS models

Usage

PTSestim(m)
PTSestim(m)

Arguments

`m`	an object of type `PTS` created with `PTSmodel`

Details

PTSestim estimates and forecasts a time series using an a PTS model

Value

The same input object with the appropriate fields filled in, in particular:

p0: Initial values for parameter search
p: Estimated parameters
lambda: Estimated Box-Cox lambda parameter
v: Estimated innovations (white noise in correctly specified models)
yFor: Forecasted values of output
yForV: Variance of forecasted values of output

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- PTSsetup(log(AirPassengers))
m1 <- PTSestim(m1)

## End(Not run)
## Not run: 
m1 <- PTSsetup(log(AirPassengers))
m1 <- PTSestim(m1)

## End(Not run)

PTSmodel

Description

Estimates and forecasts PTS general univariate models

Usage

PTSmodel(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  verbose = FALSE
)
PTSmodel(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  verbose = FALSE
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component with one or two letters: Error: ? / N / A Trend: ? / N / A / Ad / L Seasonal: ? / N / A / D (trigonometric with different variances)
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`lambda`	Box-Cox lambda parameter (NULL: estimate)
`armaIdent`	check for arma models for error component (TRUE / FALSE).
`verbose`	intermediate estimation output (TRUE / FALSE)

Details

PTSmodel is a function for modelling and forecasting univariate time series according to Power-Trend-Seasonal (PTS). It sets up the model with a number of control variables that govern the way the rest of functions in the package work. It also estimates the model parameters by Maximum Likelihood and forecasts the data. Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Value

After running PTSmodel or PTSestim:

p0: Initial values for parameter search
p: Estimated parameters
lambda: Estimated Box-Cox lambda parameter
v: Estimated innovations (white noise in correctly specified models)
yFor: Forecasted values of output
yForV: Variance of forecasted values of output

After running PTSvalidate:

table: Estimation and validation table

After running PTScomponents:

comp: Estimated components in matrix form

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- PTSmodel(log(AirPassengers))

## End(Not run)
## Not run: 
m1 <- PTSmodel(log(AirPassengers))

## End(Not run)

PTSsetup

Description

Run up PTS general univariate MSOE models

Usage

PTSsetup(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aic",
  lambda = 1,
  armaIdent = FALSE,
  verbose = FALSE
)
PTSsetup(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aic",
  lambda = 1,
  armaIdent = FALSE,
  verbose = FALSE
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component with one or two letters: Error: ? / N / A Trend: ? / N / A / Ad / L Seasonal: ? / N / A / D (trigonometric with different variances)
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`lambda`	Box-Cox lambda parameter (NULL: estimate)
`armaIdent`	check for arma models for error component (TRUE / FALSE).
`verbose`	intermediate estimation output (TRUE / FALSE)

Details

See help of PTS.

Value

After running PTSmodel or PTSestim:

p0: Initial values for parameter search
p: Estimated parameters
lambda: Estimated Box-Cox lambda parameter
v: Estimated innovations (white noise in correctly specified models)
yFor: Forecasted values of output
yForV: Variance of forecasted values of output

After running PTSvalidate:

table: Estimation and validation table

After running PTScomponents:

comp: Estimated components in matrix form

Standard methods applicable to PTS objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- PTSsetup(log(AirPassengers))

## End(Not run)
## Not run: 
m1 <- PTSsetup(log(AirPassengers))

## End(Not run)

PTSvalidate

Description

Shows a table of estimation and diagnostics results for PTS models

Usage

PTSvalidate(m, verbose = TRUE)
PTSvalidate(m, verbose = TRUE)

Arguments

`m`	an object of type `PTS` created with `PTSmodel`
`verbose`	verbose mode TRUE/FALSE

Value

The same input object with the appropriate fields filled in, in particular:

table: Estimation and validation table

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- PTSmodel(log(AirPassengers))
m1 <- PTSvalidate(m1)

## End(Not run)
## Not run: 
m1 <- PTSmodel(log(AirPassengers))
m1 <- PTSvalidate(m1)

## End(Not run)

removeNaNs

Description

Remove nans at beginning or end of vector

Usage

removeNaNs(x)
removeNaNs(x)

Arguments

`x`	a vector or a ts object

Value

vector with nans removed (only those at beginning or end)

Author(s)

Diego J. Pedregal

residuals.ETS

Description

Residuals of ETS object

Residuals of PTS object

Residuals of TETS object

Usage

## S3 method for class 'ETS'
residuals(object, ...)

## S3 method for class 'PTS'
residuals(object, ...)

## S3 method for class 'TETS'
residuals(object, ...)
## S3 method for class 'ETS'
residuals(object, ...)

## S3 method for class 'PTS'
residuals(object, ...)

## S3 method for class 'TETS'
residuals(object, ...)

Arguments

`object`	Object of class “TETS”.
`...`	Additional inputs to function.

Details

See help of ETS.

See help of PTS.

See help of TETS.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ETSmodel(log(gdp))
residuals(m1)

## End(Not run)
## Not run: 
m1 <- PTSmodel(log(AirPassengers))
residuals(m1)

## End(Not run)
## Not run: 
m1 <- TETSmodel(log(gdp))
residuals(m1)

## End(Not run)
## Not run: 
m1 <- ETSmodel(log(gdp))
residuals(m1)

## End(Not run)
## Not run: 
m1 <- PTSmodel(log(AirPassengers))
residuals(m1)

## End(Not run)
## Not run: 
m1 <- TETSmodel(log(gdp))
residuals(m1)

## End(Not run)

roots

Description

Roots of polynomial

Usage

roots(x)
roots(x)

Arguments

`x`	coefficients of polynomial in descending order

Value

Roots of polynomial

Author(s)

Diego J. Pedregal

Examples

roots(c(1, -2 ,1))
roots(conv(c(1, -1), c(1, 0.8)))
roots(c(1, -2 ,1))
roots(conv(c(1, -1), c(1, 0.8)))

rowMedians

Description

Medians of matrix by rows

Usage

rowMedians(x, na.rm = TRUE, ...)
rowMedians(x, na.rm = TRUE, ...)

Arguments

`x`	a matrix
`na.rm`	boolean indicating whether to remove nans
`...`	rest of inputs

Value

A vector with all the medians

Author(s)

Diego J. Pedregal

Examples

s <- rowMedians(matrix(4, 3, 2))
s <- rowMedians(matrix(4, 3, 2))

Sales index for large retailers in Spain

Description

Sales index for food of large retailers in Spain

Usage

sales
sales

Format

Time series objects.

Monthly data from January 1995 to December 2019

https://portal.mineco.gob.es/es-es/economiayempresa/EconomiaInformesMacro/Paginas/bdsice.aspx

Examples

## Not run: 
 sales

## End(Not run)
## Not run: 
 sales

## End(Not run)

size

Description

size of vectors or matrices

Size of vector, matrix or array

Usage

size(y)

size(y)
size(y)

size(y)

Arguments

`y`	a vector, matrix or array

Value

A vector with all the dimensions

Author(s)

Diego J. Pedregal

Examples

s <- size(matrix(4, 3, 2))
s <- size(rep(4, 3))
s <- size(array(4, c(3, 2, 2)))
s <- size(matrix(4, 3, 2))
s <- size(rep(4, 3))
s <- size(array(4, c(3, 2, 2)))

slide

Description

Rolling forecasting of a matrix of time series

Usage

slide(
  y,
  orig,
  forecFun,
  ...,
  h = 12,
  step = 1,
  output = TRUE,
  window = NA,
  parallel = FALSE
)
slide(
  y,
  orig,
  forecFun,
  ...,
  h = 12,
  step = 1,
  output = TRUE,
  window = NA,
  parallel = FALSE
)

Arguments

`y`	a vector or matrix of time series
`orig`	starting forecasting origin
`forecFun`	user function that implements forecasting methods
`...`	rest of inputs to forecFun function
`h`	forecasting horizon
`step`	observations ahead to move the forecasting origin
`output`	output TRUE/FALSE
`window`	fixed window width in number of observations (NA for non fixed)
`parallel`	run forecasts in parallel

Details

Takes a time series and run forecasting methods implemented in function forecFun h steps ahead along the time series y, starting at forecasting origin orig, and moving step observations ahead. Forecasts may be run in parallel by setting parallel to TRUE. A fixed window width may be specified with input window. The output is of dimensions (h, nOrigs, nModels, nSeries)

Value

A vector with all the dimensions

Author(s)

Diego J. Pedregal

Examples

## Not run: slide(AirPassengers, 100, forecFun)
## Not run: slide(AirPassengers, 100, forecFun)

slideAux

Description

Auxiliary function run from slide

Usage

slideAux(
  y,
  orig,
  forecFun,
  h = 12,
  step = 1,
  output = TRUE,
  graph = TRUE,
  window = NA,
  parallel = FALSE,
  ...
)
slideAux(
  y,
  orig,
  forecFun,
  h = 12,
  step = 1,
  output = TRUE,
  graph = TRUE,
  window = NA,
  parallel = FALSE,
  ...
)

Arguments

`y`	a vector or matrix of time series
`orig`	starting forecasting origin
`forecFun`	user function that implements forecasting methods
`h`	forecasting horizon
`step`	observations ahead to move the forecasting origin
`output`	output TRUE/FALSE
`graph`	fraphical output TRUE/FALSE
`window`	fixed window width in number of observations (NA for non fixed)
`parallel`	run forecasts in parallel
`...`	rest of inputs to forecFun function

Value

Next time stamp

Author(s)

Diego J. Pedregal

summary.ARIMA

Description

Prints an ARIMA object on screen

Usage

## S3 method for class 'ARIMA'
summary(object, ...)
## S3 method for class 'ARIMA'
summary(object, ...)

Arguments

`object`	Object of class “ARIMA”.
`...`	Additional inputs to function.

Details

See help of ARIMA.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ARIMAmodel(log(gdp))
summary(m1)

## End(Not run)
## Not run: 
m1 <- ARIMAmodel(log(gdp))
summary(m1)

## End(Not run)

summary.ETS

Description

Prints an ETS object on screen

Usage

## S3 method for class 'ETS'
summary(object, ...)
## S3 method for class 'ETS'
summary(object, ...)

Arguments

`object`	Object of class “ETS”.
`...`	Additional inputs to function.

Details

See help of ETS.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- ETSmodel(log(gdp))
summary(m1)

## End(Not run)
## Not run: 
m1 <- ETSmodel(log(gdp))
summary(m1)

## End(Not run)

summary.PTS

Description

Prints an PTS object on screen

Usage

## S3 method for class 'PTS'
summary(object, ...)
## S3 method for class 'PTS'
summary(object, ...)

Arguments

`object`	Object of class “PTS”.
`...`	Additional inputs to function.

Details

See help of PTS.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- PTSmodel(log(AirPassengers))
summary(m1)

## End(Not run)
## Not run: 
m1 <- PTSmodel(log(AirPassengers))
summary(m1)

## End(Not run)

summary.TETS

Description

Prints a TOBIT TETS object on screen

Usage

## S3 method for class 'TETS'
summary(object, ...)
## S3 method for class 'TETS'
summary(object, ...)

Arguments

`object`	Object of class “TETS”.
`...`	Additional inputs to function.

Details

See help of TETS.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- TETSmodel(log(gdp))
summary(m1)

## End(Not run)
## Not run: 
m1 <- TETSmodel(log(gdp))
summary(m1)

## End(Not run)

sumStats

Description

Summary statistics of a matrix of variables

Usage

sumStats(y, decimals = 5)
sumStats(y, decimals = 5)

Arguments

`y`	a vector, matrix of time series
`decimals`	number of decimals for table

Details

Position, dispersion, skewness, kurtosis, etc.

Value

Table of values

Author(s)

Diego J. Pedregal

Examples

s <- sumStats(AirPassengers)
s <- sumStats(AirPassengers)

tests

Description

Tests on a time series

Usage

tests(
  y,
  parts = 1/3,
  nCoef = min(25, length(x)/4),
  nPar = 0,
  s = frequency(y),
  avoid = 16
)
tests(
  y,
  parts = 1/3,
  nCoef = min(25, length(x)/4),
  nPar = 0,
  s = frequency(y),
  avoid = 16
)

Arguments

`y`	a vector, ts or tsibble object
`parts`	proportion of sample to include in ratio of variances test
`nCoef`	number of autocorrelation coefficients to estimate
`nPar`	number of parameters in a model if y is a residual
`s`	seasonal period, number of observations per year
`avoid`	number of observations to avoid at beginning of sample to eliminate initial effects

Details

Multiple tests on a time series, including summary statistics, autocorrelation, Gaussianity and heteroskedasticity,

Author(s)

Diego J. Pedregal

Examples

tests(AirPassengers)
tests(AirPassengers)

TETS

Description

Runs all relevant functions for TETS modelling

Usage

TETS(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(0, 1),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999,
  Ymin = -Inf,
  Ymax = Inf
)
TETS(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(0, 1),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999,
  Ymin = -Inf,
  Ymax = Inf
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component with one or two letters: Error: ? / A Trend: ? / N / A / Ad Seasonal: ? / N / A
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`forIntervals`	estimate forecasting intervals (TRUE / FALSE)
`bootstrap`	use bootstrap simulation for predictive distributions
`nSimul`	number of simulation runs for bootstrap simulation of predictive distributions
`verbose`	intermediate estimation output (TRUE / FALSE)
`alphaL`	constraints limits for alpha parameter
`betaL`	constraints limits for beta parameter
`gammaL`	constraints limits for gamma parameter
`phiL`	constraints limits for phi parameter
`p0`	initial values for parameter search (alpha, beta, phi, gamma, sigma2) with consraints:
`Ymin`	scalar or vector of time varying censoring values from below
`Ymax`	scalar or vector of time varying censoring values from above 0 < alpha < 1 0 < beta < alpha 0 < phi < 1 0 < gamma < 1 - alpha sigma2 > 0

Details

See help of TETSmodel.

Value

An object of class TETS. See TETSmodel.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPAssengers)
m1 <- TETS(y)
m1 <- TETS(y, model = "MAM")

## End(Not run)
## Not run: 
y <- log(AirPAssengers)
m1 <- TETS(y)
m1 <- TETS(y, model = "MAM")

## End(Not run)

TETScomponents

Description

Estimates components of TOBIT TETS models

Usage

TETScomponents(m)
TETScomponents(m)

Arguments

`m`	an object of type `TETS` created with `TETSmodel`

Value

The same input object with the appropriate fields filled in, in particular:

comp

Estimated components in matrix form

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- TETS(log(gdp))
m1 <- TETScomponents(m1)

## End(Not run)
## Not run: 
m1 <- TETS(log(gdp))
m1 <- TETScomponents(m1)

## End(Not run)

TETSestim

Description

Estimates and forecasts TOBIT TETS models

Usage

TETSestim(m)
TETSestim(m)

Arguments

`m`	an object of type `TETS` created with `TETSmodel`

Details

TETSestim estimates and forecasts a time series using an a TOBIT TETS model

Value

The same input object with the appropriate fields filled in, in particular:

`p`	Estimated parameters
`yFor`	Forecasted values of output
`yForV`	Variance of forecasted values of output
`ySimul`	Bootstrap simulations for forecasting distribution evaluation

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- TETSsetup(log(gdp))
m1 <- TETSestim(m1)

## End(Not run)
## Not run: 
m1 <- TETSsetup(log(gdp))
m1 <- TETSestim(m1)

## End(Not run)

TETSmodel

Description

Estimates and forecasts TOBIT TETS general univariate models

Usage

TETSmodel(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = max(2 * s, 6),
  criterion = "aicc",
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(0, 1),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999,
  Ymin = -Inf,
  Ymax = Inf
)
TETSmodel(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = max(2 * s, 6),
  criterion = "aicc",
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(0, 1),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999,
  Ymin = -Inf,
  Ymax = Inf
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component with one or two letters: Error: ? / A Trend: ? / N / A / Ad Seasonal: ? / N / A
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`forIntervals`	estimate forecasting intervals (TRUE / FALSE)
`bootstrap`	use bootstrap simulation for predictive distributions
`nSimul`	number of simulation runs for bootstrap simulation of predictive distributions
`verbose`	intermediate estimation output (TRUE / FALSE)
`alphaL`	constraints limits for alpha parameter
`betaL`	constraints limits for beta parameter
`gammaL`	constraints limits for gamma parameter
`phiL`	constraints limits for phi parameter
`p0`	initial values for parameter search (alpha, beta, phi, gamma, sigma2) with consraints:
`Ymin`	scalar or vector of time varying censoring values from below
`Ymax`	scalar or vector of time varying censoring values from above 0 < alpha < 1 0 < beta < alpha 0 < phi < 1 0 < gamma < 1 - alpha sigma2 > 0

Details

TETSmodel is a function for modelling and forecasting univariate time series with TOBIT ExponenTial Smoothing (TETS) time series models. It sets up the model with a number of control variables that govern the way the rest of functions in the package will work. It also estimates the model parameters by Maximum Likelihood and forecasts the data.

Value

An object of class TETS. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any TETS object as specified in what follows (function TETS fills in all of them at once):

After running TETSmodel or TETSestim:

`p`	Estimated parameters
`criteria`	Values for estimation criteria (LogLik, AIC, BIC, AICc)
`yFor`	Forecasted values of output
`yForV`	Variance of forecasted values of output
`ySimul`	Bootstrap simulations for forecasting distribution evaluation

After running TETSvalidate:

`table`	Estimation and validation table
`comp`	Estimated components in matrix form

After running TETScomponents:

comp

Estimated components in matrix form

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPAssengers)
m1 <- TETSmodel(y)
m1 <- TETSmodel(y, model = "A?A")

## End(Not run)
## Not run: 
y <- log(AirPAssengers)
m1 <- TETSmodel(y)
m1 <- TETSmodel(y, model = "A?A")

## End(Not run)

TETSsetup

Description

Sets up TOBIT TETS general univariate models

Usage

TETSsetup(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(0, 1),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999,
  Ymin = -Inf,
  Ymax = Inf
)
TETSsetup(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(0, 1),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999,
  Ymin = -Inf,
  Ymax = Inf
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `s` should be supplied compulsorily (see below).
`u`	a matrix of input time series. If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component with one or two letters: Error: ? / A Trend: ? / N / A / Ad Seasonal: ? / N / A
`s`	seasonal period of time series (1 for annual, 4 for quarterly, ...)
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`forIntervals`	estimate forecasting intervals (TRUE / FALSE)
`bootstrap`	use bootstrap simulation for predictive distributions
`nSimul`	number of simulation runs for bootstrap simulation of predictive distributions
`verbose`	intermediate estimation output (TRUE / FALSE)
`alphaL`	constraints limits for alpha parameter
`betaL`	constraints limits for beta parameter
`gammaL`	constraints limits for gamma parameter
`phiL`	constraints limits for phi parameter
`p0`	initial values for parameter search (alpha, beta, phi, gamma, sigma2) with consraints:
`Ymin`	scalar or vector of time varying censoring values from below
`Ymax`	scalar or vector of time varying censoring values from above 0 < alpha < 1 0 < beta < alpha 0 < phi < 1 0 < gamma < 1 - alpha sigma2 > 0

Details

See help of TETSmodel.

Value

An object of class TETS. See TETSmodel.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPAssengers)
m1 <- TETSsetup(y)
m1 <- TETSsetup(y,  model = "???")
m1 <- TETSsetup(y,  model = "?AA")

## End(Not run)
## Not run: 
y <- log(AirPAssengers)
m1 <- TETSsetup(y)
m1 <- TETSsetup(y,  model = "???")
m1 <- TETSsetup(y,  model = "?AA")

## End(Not run)

TETSvalidate

Description

Shows a table of estimation and diagnostics results for TOBIT TETS models

Usage

TETSvalidate(m)
TETSvalidate(m)

Arguments

`m`	an object of type `TETS` created with `TETSmodel`

Value

The same input object with the appropriate fields filled in, in particular:

table

Estimation and validation table

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- TETSmodel(log(gdp))
m1 <- TETSvalidate(m1)

## End(Not run)
## Not run: 
m1 <- TETSmodel(log(gdp))
m1 <- TETSvalidate(m1)

## End(Not run)

tsDisplay

Description

Displays time series plot with autocorrelation functions

Usage

tsDisplay(y, nCoef = 25, nPar = 0, s = NA)
tsDisplay(y, nCoef = 25, nPar = 0, s = NA)

Arguments

`y`	a vector, ts or tsibble object
`nCoef`	number of autocorrelation coefficients to estimate
`nPar`	number of parameters in a model if y is a residual
`s`	seasonal period, number of observations per year

Author(s)

Diego J. Pedregal

Examples

tsDisplay(AirPassengers)
tsDisplay(AirPassengers)

UC

Description

Runs all relevant functions for UC modelling

Usage

UC(
  y,
  u = NULL,
  model = "?/none/?/?",
  h = 9999,
  lambda = 1,
  outlier = 9999,
  tTest = FALSE,
  criterion = "aic",
  periods = NA,
  verbose = FALSE,
  stepwise = FALSE,
  p0 = -9999.9,
  arma = TRUE,
  TVP = NULL,
  trendOptions = "none/rw/llt/dt",
  seasonalOptions = "none/equal/different",
  irregularOptions = "none/arma(0,0)"
)
UC(
  y,
  u = NULL,
  model = "?/none/?/?",
  h = 9999,
  lambda = 1,
  outlier = 9999,
  tTest = FALSE,
  criterion = "aic",
  periods = NA,
  verbose = FALSE,
  stepwise = FALSE,
  p0 = -9999.9,
  arma = TRUE,
  TVP = NULL,
  trendOptions = "none/rw/llt/dt",
  seasonalOptions = "none/equal/different",
  irregularOptions = "none/arma(0,0)"
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `periods` should be supplied compulsorily (see below).
`u`	a matrix of external regressors included only in the observation equation. (it may be either a numerical vector or a time series object). If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component. It allows two formats "trend/seasonal/irregular" or "trend/cycle/seasonal/irregular". The possibilities available for each component are: Trend: ? / none / rw / irw / llt / dt / td; Seasonal: ? / none / equal / different; Irregular: ? / none / arma(0, 0) / arma(p, q) - with p and q integer positive orders; Cycles: ? / none / combination of positive or negative numbers. Positive numbers fix the period of the cycle while negative values estimate the period taking as initial condition the absolute value of the period supplied. Several cycles with positive or negative values are possible and if a question mark is included, the model test for the existence of the cycles specified. The following are valid examples with different meanings: 48, 48?, -48, -48?, 48+60, -48+60, -48-60, 48-60, 48+60?, -48+60?, -48-60?, 48-60?.
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`lambda`	Box-Cox transformation lambda, NULL for automatic estimation
`outlier`	critical level of outlier tests. If NA it does not carry out any outlier detection (default). A positive value indicates the critical minimum t test for outlier detection in any model during identification. Three types of outliers are identified, namely Additive Outliers (AO), Level Shifts (LS) and Slope Change (SC).
`tTest`	augmented Dickey Fuller test for unit roots used in stepwise algorithm (TRUE / FALSE). The number of models to search for is reduced, depending on the result of this test.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`periods`	vector of fundamental period and harmonics required.
`verbose`	intermediate results shown about progress of estimation (TRUE / FALSE).
`stepwise`	stepwise identification procedure (TRUE / FALSE).
`p0`	initial parameter vector for optimisation search.
`arma`	check for arma models for irregular components (TRUE / FALSE).
`TVP`	vector of zeros and ones to indicate TVP parameters.
`trendOptions`	trend models to select amongst (e.g., "rw/llt").
`seasonalOptions`	seasonal models to select amongst (e.g., "none/differentt").
`irregularOptions`	irregular models to select amongst (e.g., "none/arma(0,1)").

Details

UC is a function for modelling and forecasting univariate time series according to Unobserved Components models (UC). It sets up the model with a number of control variables that govern the way the rest of functions in the package work. It also estimates the model parameters by Maximum Likelihood, forecasts the data, performs smoothing, estimates model disturbances, estimates components and shows statistical diagnostics. Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Value

An object of class UComp. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any UComp object as specified in what follows (function UC fills in all of them at once):

After running UCmodel or UCestim:

p: Estimated parameters
v: Estimated innovations (white noise in correctly specified models)
yFor: Forecasted values of output
yForV: Forecasted values +- one standard error
criteria: Value of criteria for estimated model
iter: Number of iterations in estimation
grad: Gradient at estimated parameters
covp: Covariance matrix of parameters

After running UCvalidate:

table: Estimation and validation table

After running UCcomponents:

comp: Estimated components in matrix form
compV: Estimated components variance in matrix form

After running UCfilter, UCsmooth or UCdisturb:

yFit: Fitted values of output
yFitV: Variance of fitted values of output
a: State estimates
P: Variance of state estimates
aFor: Forecasts of states
PFor: Forecasts of states variances

After running UCdisturb:

eta: State perturbations estimates
eps: Observed perturbations estimates

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPassengers)
m1 <- UC(y)
m1 <- UC(y, model = "llt/different/arma(0,0)")

## End(Not run)
## Not run: 
y <- log(AirPassengers)
m1 <- UC(y)
m1 <- UC(y, model = "llt/different/arma(0,0)")

## End(Not run)

UCcomponents

Description

Estimates unobserved components of UC models Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Usage

UCcomponents(sys)
UCcomponents(sys)

Arguments

sys

an object of type UComp created with UC or UCmodel

Value

The same input object with the appropriate fields filled in, in particular:

comp: Estimated components in matrix form
compV: Estimated components variance in matrix form

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- UC(log(AirPassengers))
m1 <- UCcomponents(m1)

## End(Not run)
## Not run: 
m1 <- UC(log(AirPassengers))
m1 <- UCcomponents(m1)

## End(Not run)

UCdisturb

Description

Runs the Disturbance Smoother for UC models Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Usage

UCdisturb(sys)
UCdisturb(sys)

Arguments

sys

an object of type UComp created with UC

Value

The same input object with the appropriate fields filled in, in particular:

yFit: Fitted values of output
yFitV: Variance of fitted values of output
a: State estimates
P: Variance of state estimates (diagonal of covariance matrices)
eta: State perturbations estimates
eps: Observed perturbations estimates

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- UC(log(AirPassengers))
m1 <- UCdisturb(m1)

## End(Not run)
## Not run: 
m1 <- UC(log(AirPassengers))
m1 <- UCdisturb(m1)

## End(Not run)

UCestim

Description

Estimates and forecasts UC models

Usage

UCestim(sys)
UCestim(sys)

Arguments

sys

an object of type UComp created with UC

Details

UCestim estimates and forecasts a time series using an UC model. The optimization method is a BFGS quasi-Newton algorithm with a backtracking line search using Armijo conditions. Parameter names in output table are the following:

Damping: Damping factor for DT trend.
Level: Variance of level disturbance.
Slope: Variance of slope disturbance.
Rho(#): Damping factor of cycle #.
Period(#): Estimated period of cycle #.
Var(#): Variance of cycle #.
Seas(#): Seasonal harmonic with period #.
Irregular: Variance of irregular component.
AR(#): AR parameter of lag #.
MA(#): MA parameter of lag #.
AO#: Additive outlier in observation #.
LS#: Level shift outlier in observation #.
SC#: Slope change outlier in observation #.
Beta(#): Beta parameter of input #.
Cnst: Constant.

Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Value

The same input object with the appropriate fields filled in, in particular:

p: Estimated transformed parameters
v: Estimated innovations (white noise in correctly specified models)
yFor: Forecast values of output
yForV: Forecasted values variance
criteria: Value of criteria for estimated model
covp: Covariance matrix of estimated transformed parameters
grad: Gradient of log-likelihood at the optimum
iter: Estimation iterations

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- UCsetup(log(AirPassengers))
m1 <- UCestim(m1)

## End(Not run)
## Not run: 
m1 <- UCsetup(log(AirPassengers))
m1 <- UCestim(m1)

## End(Not run)

UCfilter

Description

Runs the Kalman Filter for UC models Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Usage

UCfilter(sys)
UCfilter(sys)

Arguments

sys

an object of type UComp created with UC

Value

The same input object with the appropriate fields filled in, in particular:

yFit: Fitted values of output
yFitV: Variance of fitted values of output
a: State estimates
P: Variance of state estimates (diagonal of covariance matrices)

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- UC(log(AirPassengers))
m1 <- UCfilter(m1)

## End(Not run)
## Not run: 
m1 <- UC(log(AirPassengers))
m1 <- UCfilter(m1)

## End(Not run)

UChp

Description

Hodrick-Prescott filter estimation

Usage

UChp(y, lambda = 1600)
UChp(y, lambda = 1600)

Arguments

`y`	A time series object
`lambda`	Smoothing constant (default: 1600)

Value

The cycle estimation

Author(s)

Diego J. Pedregal

Examples

## Not run: 
cycle <- UChp(USgdp)
plot(cycle)

## End(Not run)
## Not run: 
cycle <- UChp(USgdp)
plot(cycle)

## End(Not run)

UCmodel

Description

Estimates and forecasts UC general univariate models

Usage

UCmodel(
  y,
  u = NULL,
  model = "?/none/?/?",
  h = 9999,
  lambda = 1,
  outlier = 9999,
  tTest = FALSE,
  criterion = "aic",
  periods = NA,
  verbose = FALSE,
  stepwise = FALSE,
  p0 = -9999.9,
  arma = TRUE,
  TVP = NULL,
  trendOptions = "none/rw/llt/dt",
  seasonalOptions = "none/equal/different",
  irregularOptions = "none/arma(0,0)"
)
UCmodel(
  y,
  u = NULL,
  model = "?/none/?/?",
  h = 9999,
  lambda = 1,
  outlier = 9999,
  tTest = FALSE,
  criterion = "aic",
  periods = NA,
  verbose = FALSE,
  stepwise = FALSE,
  p0 = -9999.9,
  arma = TRUE,
  TVP = NULL,
  trendOptions = "none/rw/llt/dt",
  seasonalOptions = "none/equal/different",
  irregularOptions = "none/arma(0,0)"
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `periods` should be supplied compulsorily (see below).
`u`	a matrix of external regressors included only in the observation equation. (it may be either a numerical vector or a time series object). If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component. It allows two formats "trend/seasonal/irregular" or "trend/cycle/seasonal/irregular". The possibilities available for each component are: Trend: ? / none / rw / irw / llt / dt / td; Seasonal: ? / none / equal / different; Irregular: ? / none / arma(0, 0) / arma(p, q) - with p and q integer positive orders; Cycles: ? / none / combination of positive or negative numbers. Positive numbers fix the period of the cycle while negative values estimate the period taking as initial condition the absolute value of the period supplied. Several cycles with positive or negative values are possible and if a question mark is included, the model test for the existence of the cycles specified. The following are valid examples with different meanings: 48, 48?, -48, -48?, 48+60, -48+60, -48-60, 48-60, 48+60?, -48+60?, -48-60?, 48-60?.
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`lambda`	Box-Cox transformation lambda, NULL for automatic estimation
`outlier`	critical level of outlier tests. If NA it does not carry out any outlier detection (default). A positive value indicates the critical minimum t test for outlier detection in any model during identification. Three types of outliers are identified, namely Additive Outliers (AO), Level Shifts (LS) and Slope Change (SC).
`tTest`	augmented Dickey Fuller test for unit roots used in stepwise algorithm (TRUE / FALSE). The number of models to search for is reduced, depending on the result of this test.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`periods`	vector of fundamental period and harmonics required.
`verbose`	intermediate results shown about progress of estimation (TRUE / FALSE).
`stepwise`	stepwise identification procedure (TRUE / FALSE).
`p0`	initial parameter vector for optimisation search.
`arma`	check for arma models for irregular components (TRUE / FALSE).
`TVP`	vector of zeros and ones to indicate TVP parameters.
`trendOptions`	trend models to select amongst (e.g., "rw/llt").
`seasonalOptions`	seasonal models to select amongst (e.g., "none/differentt").
`irregularOptions`	irregular models to select amongst (e.g., "none/arma(0,1)").

Details

UCmodel is a function for modelling and forecasting univariate time series according to Unobserved Components models (UC). It sets up the model with a number of control variables that govern the way the rest of functions in the package work. It also estimates the model parameters by Maximum Likelihood and forecasts the data. Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Value

After running UCmodel or UCestim:

p: Estimated parameters
v: Estimated innovations (white noise in correctly specified models)
yFor: Forecasted values of output
yForV: Forecasted values +- one standard error
criteria: Value of criteria for estimated model
iter: Number of iterations in estimation
grad: Gradient at estimated parameters
covp: Covariance matrix of parameters

After running UCvalidate:

table: Estimation and validation table

After running UCcomponents:

comp: Estimated components in matrix form
compV: Estimated components variance in matrix form

After running UCfilter, UCsmooth or UCdisturb:

yFit: Fitted values of output
yFitV: Variance of fitted values of output
a: State estimates
P: Variance of state estimates
aFor: Forecasts of states
PFor: Forecasts of states variances

After running UCdisturb:

eta: State perturbations estimates
eps: Observed perturbations estimates

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPassengers)
m1 <- UCmodel(y)
m1 <- UCmodel(y, model = "llt/equal/arma(0,0)")

## End(Not run)
## Not run: 
y <- log(AirPassengers)
m1 <- UCmodel(y)
m1 <- UCmodel(y, model = "llt/equal/arma(0,0)")

## End(Not run)

UComp

Description

Package for time series modelling and forecasting of times series models inspired on different sources:

Details

Unobserved Components models due to A.C. Harvey (Basic Structural Model: BSM), enhanced with automatic identification tools by Diego J. Pedregal.
ExponenTial Smoothing by R.J. Hyndman and colaborators.
ARIMA models by V. Gómez and A. Maravall
Tobit ETS models by Pedregal, Trapero and Holgado

The package is designed for automatic identification among a wide range of possible models. The models may include exogenous variables. ARMA irregular components and automatic detection of outliers in some instances.

References

Harvey AC (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cam- bridge University Press.

de Jong, P & Penzer, J (1998). Diagnosing Shocks in Time Series, Journal of the American Statistical Association, 93, 442, 796-806.

Pedregal, DJ, & Young, PC (2002). Statistical approaches to modelling and forecasting time series. In M. Clements, & D. Hendry (Eds.), Companion to economic forecasting (pp. 69–104). Oxford: Blackwell Publishers.

Durbin J, Koopman SJ (2012). Time Series Analysis by State Space Methods. 38. Oxford University Press.

Proietti T and Luati A (2013). Maximum likelihood estimation of time series models: the Kalman filter and beyond, in Handbook of research methods and applications in empirical macroeconomics, ed. Nigar Hashimzade and Michael Thornton, E. Elgar, UK.

Hyndman RJ, Koehler AB, Ord JK and Snyder RD (2008), Forecasting with exponential smoothing, The State Sapce approach, Berlin, Springer-Verlag.

Gómez V and Maravall, A (2000), Automatic methods for univariate series. In Peña, D., Tiao, G.C. and Tsay R.S., A course in time series analyis. Wiley.

Trapero JR, Holgado E, Pedregal DJ (2024), Demand forecasting under lost sales stock policies, International Journal of Forecasting, 40, 1055-1068.

Maintainer

Diego J. Pedregal

Author(s)

Diego J. Pedregal

UCsetup

Description

Sets up UC general univariate models

Usage

UCsetup(
  y,
  u = NULL,
  model = "?/none/?/?",
  h = 9999,
  lambda = 1,
  outlier = 9999,
  tTest = FALSE,
  criterion = "aic",
  periods = NA,
  verbose = FALSE,
  stepwise = FALSE,
  p0 = -9999.9,
  arma = FALSE,
  TVP = NULL,
  trendOptions = "none/rw/llt/dt",
  seasonalOptions = "none/equal/different",
  irregularOptions = "none/arma(0,0)"
)
UCsetup(
  y,
  u = NULL,
  model = "?/none/?/?",
  h = 9999,
  lambda = 1,
  outlier = 9999,
  tTest = FALSE,
  criterion = "aic",
  periods = NA,
  verbose = FALSE,
  stepwise = FALSE,
  p0 = -9999.9,
  arma = FALSE,
  TVP = NULL,
  trendOptions = "none/rw/llt/dt",
  seasonalOptions = "none/equal/different",
  irregularOptions = "none/arma(0,0)"
)

Arguments

`y`	a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input `periods` should be supplied compulsorily (see below).
`u`	a matrix of external regressors included only in the observation equation. (it may be either a numerical vector or a time series object). If the output wanted to be forecast, matrix `u` should contain future values for inputs.
`model`	the model to estimate. It is a single string indicating the type of model for each component. It allows two formats "trend/seasonal/irregular" or "trend/cycle/seasonal/irregular". The possibilities available for each component are: Trend: ? / none / rw / irw / llt / dt / td; Seasonal: ? / none / equal / different; Irregular: ? / none / arma(0, 0) / arma(p, q) - with p and q integer positive orders; Cycles: ? / none / combination of positive or negative numbers. Positive numbers fix the period of the cycle while negative values estimate the period taking as initial condition the absolute value of the period supplied. Several cycles with positive or negative values are possible and if a question mark is included, the model test for the existence of the cycles specified. The following are valid examples with different meanings: 48, 48?, -48, -48?, 48+60, -48+60, -48-60, 48-60, 48+60?, -48+60?, -48-60?, 48-60?.
`h`	forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
`lambda`	Box-Cox transformation lambda, NULL for automatic estimation
`outlier`	critical level of outlier tests. If NA it does not carry out any outlier detection (default). A positive value indicates the critical minimum t test for outlier detection in any model during identification. Three types of outliers are identified, namely Additive Outliers (AO), Level Shifts (LS) and Slope Change (SC).
`tTest`	augmented Dickey Fuller test for unit roots used in stepwise algorithm (TRUE / FALSE). The number of models to search for is reduced, depending on the result of this test.
`criterion`	information criterion for identification ("aic", "bic" or "aicc").
`periods`	vector of fundamental period and harmonics required.
`verbose`	intermediate results shown about progress of estimation (TRUE / FALSE).
`stepwise`	stepwise identification procedure (TRUE / FALSE).
`p0`	initial parameter vector for optimisation search.
`arma`	check for arma models for irregular components (TRUE / FALSE).
`TVP`	vector of zeros and ones to indicate TVP parameters.
`trendOptions`	trend models to select amongst (e.g., "rw/llt").
`seasonalOptions`	seasonal models to select amongst (e.g., "none/differentt").
`irregularOptions`	irregular models to select amongst (e.g., "none/arma(0,1)").

Details

See help of UC.

Value

After running UCmodel or UCestim:

p: Estimated parameters
v: Estimated innovations (white noise in correctly specified models)
yFor: Forecasted values of output
yForV: Variance of forecasts
criteria: Value of criteria for estimated model
iter: Number of iterations in estimation
grad: Gradient at estimated parameters
covp: Covariance matrix of parameters

After running UCvalidate:

table: Estimation and validation table

After running UCcomponents:

comp: Estimated components in matrix form
compV: Estimated components variance in matrix form

After running UCfilter, UCsmooth or UCdisturb:

yFit: Fitted values of output
yFitV: Estimated fitted values variance
a: State estimates
P: Variance of state estimates
aFor: Forecasts of states
PFor: Forecasts of states variances

After running UCdisturb:

eta: State perturbations estimates
eps: Observed perturbations estimates

Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Author(s)

Diego J. Pedregal

Examples

## Not run: 
y <- log(AirPassengers)
m1 <- UCsetup(y)
m1 <- UCsetup(y, outlier = 4)
m1 <- UCsetup(y, model = "llt/equal/arma(0,0)")
m1 <- UCsetup(y, model = "?/?/?/?")
m1 <- UCsetup(y, model = "llt/?/equal/?", outlier = 4)

## End(Not run)
## Not run: 
y <- log(AirPassengers)
m1 <- UCsetup(y)
m1 <- UCsetup(y, outlier = 4)
m1 <- UCsetup(y, model = "llt/equal/arma(0,0)")
m1 <- UCsetup(y, model = "?/?/?/?")
m1 <- UCsetup(y, model = "llt/?/equal/?", outlier = 4)

## End(Not run)

UCsmooth

Description

Runs the Fixed Interval Smoother for UC models Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Usage

UCsmooth(sys)
UCsmooth(sys)

Arguments

sys

an object of type UComp created with UC

Value

The same input object with the appropriate fields filled in, in particular:

yFit: Fitted values of output
yFitV: Variance of fitted values of output
a: State estimates
P: Variance of state estimates (diagonal of covariance matrices)

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- UC(log(AirPassengers))
m1 <- UCsmooth(m1)

## End(Not run)
## Not run: 
m1 <- UC(log(AirPassengers))
m1 <- UCsmooth(m1)

## End(Not run)

UCvalidate

Description

Shows a table of estimation and diagnostics results for UC models. Equivalent to print or summary. The table shows information in four sections: Firstly, information about the model estimated, the relevant periods of the seasonal component included, and further information about convergence. Secondly, parameters with their names are provided, the asymptotic standard errors, the ratio of the two, and the gradient at the optimum. One asterisk indicates concentrated-out parameters and two asterisks signals parameters constrained during estimation. Thirdly, information criteria and the value of the log-likelihood. Finally, diagnostic statistics about innovations, namely, the Ljung-Box Q test of absense of autocorrelation statistic for several lags, the Jarque-Bera gaussianity test, and a standard ratio of variances test.

Usage

UCvalidate(sys, printScreen = TRUE)
UCvalidate(sys, printScreen = TRUE)

Arguments

`sys`	an object of type `UComp` created with `UC`
`printScreen`	print to screen or just return output table

Value

The same input object with the appropriate fields filled in, in particular:

table: Estimation and validation table

Author(s)

Diego J. Pedregal

Examples

## Not run: 
m1 <- UC(log(gdp))
m1 <- UCvalidate(m1)

## End(Not run)
## Not run: 
m1 <- UC(log(gdp))
m1 <- UCvalidate(m1)

## End(Not run)

US GDP

Description

Seasonally adjusted quarterly US real gross domestic product (USgdp).

Usage

USgdp
USgdp

Format

Time series objects.

Quarterly data from 1962 to 2019

Source

USgdp

Examples

## Not run: 
 USgdp

## End(Not run)
## Not run: 
 USgdp

## End(Not run)

varTest

Description

Ratio of variances test

Usage

varTest(y, parts = 1/3)
varTest(y, parts = 1/3)

Arguments

`y`	a vector, ts or tsibble object
`parts`	portion of sample to estimate variances

Value

Table with test results

Author(s)

Diego J. Pedregal

Examples

varTest(AirPassengers)
varTest(AirPassengers)

zplane

Description

Real-imaginary plane to show roots of digital filters (ARMA)

Usage

zplane(MApoly = 1, ARpoly = 1)
zplane(MApoly = 1, ARpoly = 1)

Arguments

`MApoly`	coefficients of numerator polynomial in descending order
`ARpoly`	coefficients of denominator polynomial in descending order

Details

Shows the real-imaginary plane to show zeros (roots of numerator or MA polynomial) and poles (roots of denominator of AR polynomial). Unit roots and real vs imaginary roots can be seen by eye

Author(s)

Diego J. Pedregal

Examples

zplane(c(1, -2, 1), c(1, -0.8))
zplane(c(1, -2, 1), c(1, -0.8))

Package 'UComp'

Help Index

Accuracy

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

acft

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

AIC.UComp

Description

Usage

Arguments

Details

Author(s)

See Also

Examples

Airpassengers in Spain

Description

Usage

Format

Examples

ARIMA

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

ARIMAestim

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

ARIMAmodel

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

ARIMAsetup

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

ARIMAvalidate

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

arma2tsi

Description

Usage

Arguments

Author(s)