Package 'RJDemetra'

Title: Interface to 'JDemetra+' Seasonal Adjustment Software
Description: Interface around 'JDemetra+' (<https://github.com/jdemetra/jdemetra-app>), the seasonal adjustment software officially recommended to the members of the European Statistical System (ESS) and the European System of Central Banks. It offers full access to all options and outputs of 'JDemetra+', including the two leading seasonal adjustment methods TRAMO/SEATS+ and X-12ARIMA/X-13ARIMA-SEATS.
Authors: Alain Quartier-la-Tente [aut, cre] , Anna Michalek [aut], Jean Palate [aut], Raf Baeyens [aut]
Maintainer: Alain Quartier-la-Tente <[email protected]>
License: EUPL
Version: 0.2.7
Built: 2024-11-01 06:26:25 UTC
Source: CRAN

Help Index


Add a seasonally adjusted series to a multi-processing

Description

Function to add a new seasonally adjusted object (class "SA" or "jSA") to a workspace object.

Usage

add_sa_item(workspace, multiprocessing, sa_obj, name)

Arguments

workspace

the workspace to add the seasonally adjusted series to.

multiprocessing

the name or index of the multiprocessing to add the seasonally adjusted series to.

sa_obj

the seasonally adjusted object to add

name

the name of the seasonally adjusted series in the multiprocessing. By default the name of the sa_obj is used.

See Also

load_workspace, save_workspace

Examples

dir <- tempdir()
# Adjustment of a series with the x13 and Tramo-Seats methods
spec_x13 <- x13_spec(spec = "RSA5c", easter.enabled = FALSE)
sa_x13 <- x13(ipi_c_eu[, "FR"], spec = spec_x13)
spec_ts <- tramoseats_spec(spec = "RSA5")
sa_ts <- jtramoseats(ipi_c_eu[, "FR"], spec = spec_ts)

# Creation of a new workspace..
wk <- new_workspace()
# and of the multiprocessing "sa1" that will contain the series
new_multiprocessing(wk, "sa1")
# Addition of the adjusted series to the workspace via the sa1 multiprocessing
add_sa_item(wk, "sa1", sa_x13, "X13")
add_sa_item(wk, "sa1", sa_ts, "TramoSeats")

# Export of the new filled workspace
save_workspace(wk, file.path(dir, "workspace.xml"))

Compute a workspace multi-processing(s)

Description

Function to compute all the multiprocessings or only a given one from a workspace. By default, the workspace only contains definitions: computation is needed to recalculate and access the adjusted model (with get_model).

Usage

compute(workspace, i)

Arguments

workspace

the workspace to compute.

i

a character or numeric indicating the name or the index of the multiprocessing to compute. By default, all multiprocessings are computed.

See Also

get_model

Examples

spec_x13 <- x13_spec(spec = "RSA5c", easter.enabled = FALSE)
sa_x13 <- x13(ipi_c_eu[, "FR"], spec = spec_x13)

wk <- new_workspace()
mp <- new_multiprocessing(wk, "sap1")
add_sa_item(wk, "sap1", sa_x13, "X13")
sa_item1 <- get_object(mp, 1)

get_model(sa_item1, wk) # Returns NULL

compute(wk)

get_model(sa_item1, wk) # Returns the SA model sa_x13

Count the number of objects inside a workspace or multiprocessing

Description

Generic functions to count the number of multiprocessing (respectively sa_item) inside a workspace (respectively multiprocessing).

Usage

count(x)

Arguments

x

the workspace or the multiprocessing.

See Also

Other functions to retrieve information from a workspace, multiprocessing or sa_item: get_model, get_name, get_ts.

Examples

wk <- new_workspace()
mp <- new_multiprocessing(wk, "sap1")
count(wk) # 1 multiprocessing inside the workspace wk
count(mp) # 0 sa_item inside the multiprocessing mp

Get the Java name of all the contained object

Description

Generic functions to retrieve the Java name of the contained multiprocessings or the contained sa_items.

Usage

get_all_names(x)

Arguments

x

An object containing other objects whose names we want to know

Value

A character vector containing all the names.

See Also

Other functions to retrieve information from a workspace, multiprocessing or sa_item: get_name, get_position, count, get_model, get_ts.

Examples

spec_x13 <- x13_spec(spec = "RSA5c", easter.enabled = FALSE)
sa_x13 <- x13(ipi_c_eu[, "FR"], spec = spec_x13)
spec_ts <- tramoseats_spec(spec = "RSA5")
sa_ts <- tramoseats(ipi_c_eu[, "FR"], spec = spec_ts)

wk <- new_workspace()
mp <- new_multiprocessing(wk, "sap1")
mp2 <- new_multiprocessing(wk, "sap2")

get_all_names(wk)

add_sa_item(wk, "sap1", sa_x13, "X13")
add_sa_item(wk, "sap1", sa_ts, "TramoSeats")

get_all_names(mp)

Get the seasonally adjusted model from a workspace

Description

Generic functions to retrieve seasonally adjusted model(s) from workspace, multiprocessing or sa_item object. get_model returns a "SA" object while get_jmodel returns the Java objects of the models.

Usage

get_jmodel(x, workspace, userdefined = NULL, progress_bar = TRUE)

get_model(x, workspace, userdefined = NULL, progress_bar = TRUE)

Arguments

x

the object from which to retrieve the seasonally adjusted model.

workspace

the workspace object where models are stored. If x is a workspace object, this parameter is not used.

userdefined

a vector containing the names of additional output variables. (see x13 or tramoseats).

progress_bar

Boolean: if TRUE, a progress bar is printed.

Value

get_model() returns a seasonally adjusted object (class c("SA", "X13") or c("SA", "TRAMO_SEATS") or a list of seasonally adjusted objects:

  • if x is a sa_item object, get_model(x) returns a "SA" object (or a jSA object with get_jmodel(x));

  • if x is a multiprocessing object, get_ts(x) returns a list of length the number of sa_items, each element containing a "SA" object (or a jSA object with get_jmodel(x));

  • if x is a workspace object, get_ts(x) returns list of length the number of multiprocessings, each element containing a list of "SA" object(s) (or jSA object's) with get_jmodel(x)).

See Also

Other functions to retrieve information from a workspace, multiprocessing or sa_item: count, get_name, get_ts.

compute

Examples

spec_x13 <- x13_spec(spec = "RSA5c", easter.enabled = FALSE)
sa_x13 <- x13(ipi_c_eu[, "FR"], spec = spec_x13)
spec_ts <- tramoseats_spec(spec = "RSA5")
sa_ts <- tramoseats(ipi_c_eu[, "FR"], spec = spec_ts)

wk <- new_workspace()
mp <- new_multiprocessing(wk, "sap1")
add_sa_item(wk, "sap1", sa_x13, "X13")
add_sa_item(wk, "sap1", sa_ts, "TramoSeats")

compute(wk) # It's important to compute the workspace before retrieving the SA model
sa_item1 <- get_object(mp, 1)

get_model(sa_item1, wk) # To extract the model of the sa_item1: its the object sa_x13

# To get all models from the multiprocessing mp:
get_model(mp, wk)

# To get all models from the workspace wk:
get_model(wk)

Get the Java name of a multiprocessing or a sa_item

Description

Generic functions to retrieve the Java name of a multiprocessing or a sa_item.

Usage

get_name(x)

Arguments

x

the object to retrieve the name from.

Value

A character.

See Also

Other functions to retrieve information from a workspace, multiprocessing or sa_item: count, get_model, get_ts.

Examples

spec_x13 <- x13_spec(spec = "RSA5c", easter.enabled = FALSE)
sa_x13 <- x13(ipi_c_eu[, "FR"], spec = spec_x13)
spec_ts <- tramoseats_spec(spec = "RSA5")
sa_ts <- tramoseats(ipi_c_eu[, "FR"], spec = spec_ts)

wk <- new_workspace()
mp <- new_multiprocessing(wk, "sap1")
add_sa_item(wk, "sap1", sa_x13, "X13")
add_sa_item(wk, "sap1", sa_ts, "TramoSeats")

sa_item1 <- get_object(mp, 1)
sa_item2 <- get_object(mp, 2)

get_name(sa_item1) # returns "X13"
get_name(sa_item2) # returns "TramoSeats"

get_name(mp) # returns "sap1"

# To retrieve the name of every sa_item in a given multiprocessing:
sapply(get_all_objects(mp), get_name)

# To retrieve the name of every multiprocessing in a given workspace:
sapply(get_all_objects(wk), get_name)

# To retrieve the name of every sa_item in a given workspace:
lapply(get_all_objects(wk),function(mp){
  sapply(get_all_objects(mp), get_name)
})

Get objects inside a workspace or multiprocessing

Description

Generic functions to retrieve all (get_all_objects()) multiprocessing (respectively sa_item) from a workspace (respectively multiprocessing) or to retrieve a single one (get_object()) .

Usage

get_object(x, pos = 1)

get_all_objects(x)

Arguments

x

the object in which to store the extracted multiprocessing or sa_item.

pos

the index of the object to extract.

Value

An object of class multiprocessing or sa_item (for get_object()) or a list of objects of class multiprocessing or sa_item (for get_all_objects()).

See Also

Other functions to retrieve information from a workspace, multiprocessing or sa_item: count, get_model, get_name, get_ts.

Examples

sa_x13 <- x13(ipi_c_eu[, "FR"], spec = "RSA5c")

wk <- new_workspace()
mp <- new_multiprocessing(wk, "sap1")
add_sa_item(wk, "sap1", sa_x13, "X13")

# A way to retrieve the multiprocessing:
mp <- get_object(wk, 1)
# And the sa_item object:
sa_item <- get_object(mp, 1)

Get the position of an object

Description

Generic functions to retrieve the position of the contained multiprocessings or the contained sa_items.

Usage

get_position(x, name)

Arguments

x

An object containing other objects whose names we want to know

name

acharacter specifiing an object

Value

A integer

See Also

Other functions to retrieve information from a workspace, multiprocessing or sa_item: get_name, get_all_names, count, get_model, get_ts.

Examples

spec_x13 <- x13_spec(spec = "RSA5c", easter.enabled = FALSE)
sa_x13 <- x13(ipi_c_eu[, "FR"], spec = spec_x13)
spec_ts <- tramoseats_spec(spec = "RSA5")
sa_ts <- tramoseats(ipi_c_eu[, "FR"], spec = spec_ts)

wk <- new_workspace()
mp <- new_multiprocessing(wk, "sap1")
mp2 <- new_multiprocessing(wk, "sap2")

get_position(wk, "sap1")
get_position(wk, "sap2")

add_sa_item(wk, "sap1", sa_x13, "X13")
add_sa_item(wk, "sap1", sa_ts, "TramoSeats")

get_position(mp, "TramoSeats")
get_position(mp, "X13")

Get the input raw time series

Description

Generic functions to retrieve the input raw time series of a workspace, multiprocessing, sa_item or SA object.

Usage

get_ts(x)

Arguments

x

the object from which to retrieve the time series.

Value

get_ts() returns a ts object or list of ts objects:

  • if x is a sa_item or a SA object, get_ts(x) returns a single ts object;

  • if x is a multiprocessing object, get_ts(x) returns a list of length the number of sa_items, each element being a ts object;

  • if x is a workspace object, get_ts(x) returns a list of length the number of multiprocessings, each element being a list of ts objects.

See Also

Other functions to retrieve information from a workspace, multiprocessing or sa_item: count, get_model, get_name.

Examples

sa_x13 <- x13(ipi_c_eu[, "FR"], spec = "RSA5c")

wk <- new_workspace()
mp <- new_multiprocessing(wk, "sap1")
add_sa_item(wk, "sap1", sa_x13, "X13")
sa_item <- get_object(mp, 1)

  # Extracting the raw time series from an adjusted series:
get_ts(sa_x13) # Returns the ts object ipi_c_eu[, "FR"]

  # Extracting the raw time series from a sa_item:
get_ts(sa_item) # Returns the ts object ipi_c_eu[, "FR"]

  # Extracting all raw time series from a multiprocessing:
# Returns a list of length 1 named "X13" containing the ts object ipi_c_eu[, "FR"]:
get_ts(mp)


  # Extracting all raw time series from a workspace:
# Returns a list of length 1 named "sap1" containing a list
# of length 1 named "X13", containing the ts object ipi_c_eu[, "FR"]
get_ts(wk)

Industrial Production Indices in manufacturing industry in the European Union

Description

A dataset containing on monthly industrial production indices in manufacturing in the European Union (from sts_inpr_m dataset of Eurostat). Data are based 100 in 2015 and are unadjusted, i.e. neither seasonally adjusted nor calendar adjusted.

Usage

ipi_c_eu

Format

A monthly ts object from January 1990 to December 2020 with 34 variables.

Details

The dataset contains 34 time series corresponding to the following geographical area

BE Belgium
BG Bulgaria
CZ Czech Republic
DK Denmark
DE Germany (until 1990 former territory of the FRG)
EE Estonia
IE Ireland
EL Greece
ES Spain
FR France
HR Croatia
IT Italy
CY Cyprus
LV Latvia
LT Lithuania
LU Luxembourg
HU Hungary
MT Malta
NL Netherlands
AT Austria
PL Poland
PT Portugal
RO Romania
SI Slovenia
SK Slovakia
FI Finland
SE Sweden
UK United Kingdom
NO Norway
CH Switzerland
ME Montenegro
MK Former Yugoslav Republic of Macedonia, the
RS Serbia
TR Turkey
BA Bosnia and Herzegovina

Source

Eurostat, 'sts_inpr_m' database.


Functions around 'jSA' objects

Description

get_dictionary returns the indicators that can be extracted from "jSA" objects, get_indicators extracts a list of indicators jSA2R returns the corresponding "SA".

Usage

get_jspec(x, ...)

get_dictionary(x)

get_indicators(x, ...)

jSA2R(x, userdefined = NULL)

Arguments

x

a "jSA" object.

...

characters containing the names of the indicators to extract.

userdefined

a userdefined vector containing the names of additional output variables (see user_defined_variables). Only used for "SA" objects.

Details

A "jSA" object is a list of three elements:

  • "result": the Java object containing the results of a seasonal adjustment or a pre-adjustment method.

  • "spec": the Java object containing the specification of a seasonal adjustment or a pre-adjustment method.

  • "dictionary": the Java object containing the dictionary of a seasonal adjustment or a pre-adjustment method. In particular, it contains all the user-defined regressors.

get_dictionary returns the list of indicators that can be extracted from a jSA object by the function get_indicators.

jSA2R returns the corresponding formatted seasonally adjusted ("SA" object) or RegARIMA ("regarima" object) model.

get_jspec returns the Java object that contains the specification of an object. Such object can be of type "jSA", "X13", "TRAMO_SEATS" or "sa_item".

Value

get_dictionary returns a vector of characters, get_indicators returns a list containing the indicators that are extracted, jSA2R returns a "SA" or a "regarima" object and get_jspec returns a Java object.

Examples

myseries <- ipi_c_eu[, "FR"]
mysa <- jx13(myseries, spec = "RSA5c")
get_dictionary(mysa)

get_indicators(mysa, "decomposition.b2", "decomposition.d10")

# To convert the Java object to an R object
jSA2R(mysa)

Load a 'JDemetra+' workspace

Description

Function to load a 'JDemetra+' workspace.

Usage

load_workspace(file)

Arguments

file

the path to the 'JDemetra+' workspace to load. By default a dialog box opens.

Value

An object of class "workspace".

See Also

save_workspace, get_model


Create a workspace or a multi-processing

Description

Functions to create a 'JDemetra+' workspace (new_workspace()) and to add a new multi-processing (new_multiprocessing()).

Usage

new_workspace()

new_multiprocessing(workspace, name)

Arguments

workspace

a workspace object

name

character name of the new multiprocessing

Value

new_workspace() returns an object of class workspace and new_multiprocessing() returns an object of class multiprocessing.

See Also

load_workspace, save_workspace, add_sa_item

Examples

# To create and export an empty 'JDemetra+' workspace
wk <- new_workspace()
mp <- new_multiprocessing(wk, "sa1")

Plotting regarima, decomposition or final results of a SA

Description

Plotting methods for the S3 class objects around the seasonal adjustment: "regarima" for RegARIMA,"decomposition_X11" and "decomposition_SEATS" for the decomposition with X13 and TRAMO-SEATS, "final" for the final SA results and "SA" for the entire seasonal adjustment object. The function plot.SA just calls the function plot.final.

Usage

## S3 method for class 'regarima'
plot(
  x,
  which = 1:6,
  caption = list("Residuals", "Histogram of residuals", "Normal Q-Q", "ACF of residuals",
    "PACF of residuals", "Decomposition", list("Y linearised", "Calendar effects",
    "Outliers effects"))[sort(which)],
  ask = prod(par("mfcol")) < length(which) && dev.interactive(),
  ...
)

## S3 method for class 'decomposition_X11'
plot(x, first_date, last_date, caption = "S-I ratio", ylim, ...)

## S3 method for class 'decomposition_SEATS'
plot(x, first_date, last_date, caption = "S-I ratio", ylim, ...)

## S3 method for class 'final'
plot(
  x,
  first_date,
  last_date,
  forecast = TRUE,
  type_chart = c("sa-trend", "cal-seas-irr"),
  caption = c(`sa-trend` = "Y, Sa, trend", `cal-seas-irr` =
    "Cal., sea., irr.")[type_chart],
  ask = length(type_chart) > 1 && dev.interactive(),
  ylim,
  ...
)

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

Arguments

x

the object to plot

which

a numeric vector specifying which graphs should be plotted: (1) "Residuals", (2) "Histogram of residuals", (3) "Normal Q-Q", (4) "ACF of residuals", (5) "PACF of residuals", (6) "Decomposition", (7) "Decomposition - zoom"

caption

a string containing the graph title

ask

a Boolean. If TRUE, the user will be prompted before a new graphical page is started.

...

other parameters

first_date

the plot starting date. If missing, the plot starts at the beginning of the time-series.

last_date

the end date of the plot. If missing, the plot ends at the end of the time-series (eventually, including forecast).

ylim

the y limits of the plot.

forecast

a Boolean indicating if forecasts should be included in the plot. If TRUE, the forecast is plotted.

type_chart

a string indicating which type of chart to plot

Examples

myseries <- ipi_c_eu[, "FR"]
mysa <- x13(myseries, spec = c("RSA5c"))
  # RegArima
plot(mysa$regarima) # 6 graphics are plotted by default
# To plot only one graphic (here, the residuals) and change the title:
plot(mysa$regarima, which = 1, caption = "Plot of residuals")
plot(mysa$regarima, which = 7)

  # Decomposition
plot(mysa$decomposition) # To plot the S-I ratio
plot(mysa$decomposition, first_date = c(2010, 1)) # To start the plot in January 2010

  # Final
plot(mysa$final) # 2 graphics are plotted by default
# To only plot one graphic (here the raw data, the seasonally adjusted data and the trend),
# To change the last date and the title
plot(mysa$final, last_date = c(2000, 1),
     caption = "Results", type_chart = "sa-trend")

RegARIMA model, pre-adjustment in X13 and TRAMO-SEATS

Description

The regarima/regarima_x13/regarima_tramoseats functions remove deterministic effects from the input series (e.g.calendar effects, outliers) using a multivariate regression model with arima errors. The jregarima/jregarima_x13/jregarima_tramoseats functions do the same computation but return the Java objects instead of a formatted output.

Usage

jregarima(series, spec = NA)

jregarima_tramoseats(
  series,
  spec = c("TRfull", "TR0", "TR1", "TR2", "TR3", "TR4", "TR5")
)

jregarima_x13(series, spec = c("RG5c", "RG0", "RG1", "RG2c", "RG3", "RG4c"))

regarima(series, spec = NA)

regarima_tramoseats(
  series,
  spec = c("TRfull", "TR0", "TR1", "TR2", "TR3", "TR4", "TR5")
)

regarima_x13(series, spec = c("RG5c", "RG0", "RG1", "RG2c", "RG3", "RG4c"))

Arguments

series

an univariate time series

spec

the model specification. For the function:

  • regarima: an object of class c("regarima_spec","X13") or c("regarima_spec","TRAMO_SEATS"). See the functions regarima_spec_x13 and regarima_spec_tramoseats.

  • regarima_x13: the name of a predefined X13 'JDemetra+' model specification (see Details). The default value is "RG5c".

  • regarima_tramoseats:the name of a predefined TRAMO-SEATS 'JDemetra+' model specification (see Details). The default value is "TRfull".

Details

When seasonally adjusting with X13 and TRAMO-SEATS, the first step consists in pre-adjusting the original series with a RegARIMA model, where the original series is corrected for any deterministic effects and missing observations. This step is also referred to as the linearization of the original series.

The RegARIMA model (model with ARIMA errors) is specified as such:

zt=ytβ+xtz_t = y_t\beta + x_t

where:

  • ztz_t is the original series;

  • β=(β1,...,βn)\beta = (\beta_1,...,\beta_n) is a vector of regression coefficients;

  • yt=(y1t,...,ynt)y_t = (y_{1t},...,y_{nt}) are nn regression variables (outliers, calendar effects, user-defined variables);

  • xtx_t is a disturbance that follows the general ARIMA process: ϕ(B)δ(B)xt=θ(B)at\phi(B)\delta(B)x_t = \theta(B)a_t; where ϕ(B),δ(B)\phi(B), \delta(B) and θ(B)\theta(B) are finite polynomials in BB and ata_t is a white noise variable with zero mean and a constant variance.

The polynomial ϕ(B)\phi(B) is a stationary autoregressive (AR) polynomial in BB, which is a product of the stationary regular AR polynomial in BB and the stationary seasonal polynomial in BsB^s:

ϕ(B)=ϕp(B)Φbp(Bs)=(1+ϕ1B+...+ϕpBp)(1+Φ1Bs+...+ΦbpBbps)\phi(B)=\phi_p(B)\Phi_{bp}(B^s)=(1+\phi_1B+...+\phi_pB^p)(1+\Phi_1B^s+...+\Phi_{bp}B^{bps})

where:

  • pp is the number of regular AR terms (here and in 'JDemetra+', p3p \le 3);

  • bpbp is the number of seasonal AR terms (here and in 'JDemetra+', bp1bp \le 1);

  • ss is the number of observations per year (ie. The time series frequency).

The polynomial θ(B)\theta(B) is an invertible moving average (MA) polynomial in BB, which is a product of the invertible regular MA polynomial in BB and the invertible seasonal MA polynomial in BsB^s:

θ(B)=θq(B)Θbq(Bs)=(1+θ1B+...+θqBq)(1+Θ1Bs+...+ΘbqBbqs)\theta(B)=\theta_q(B)\Theta_{bq}(B^s)=(1+\theta_1B+...+\theta_qB^q)(1+\Theta_1B^s+...+\Theta_{bq}B^{bqs})

where:

  • qq is the number of regular MA terms (here and in 'JDemetra+', q3q \le 3);

  • bqbq is the number of seasonal MA terms (here and in 'JDemetra+', bq1bq \le 1).

The polynomial δ(B)\delta(B) is the non-stationary AR polynomial in BB (unit roots):

δ(B)=(1B)d(1Bs)ds\delta(B) = (1-B)^d(1-B^s)^{d_s}

where:

  • dd is the regular differencing order (here and in 'JDemetra+', d1d \le 1);

  • dsd_s is the seasonal differencing order (here and in 'JDemetra+', ds1d_s \le 1).

NB. The notations used for AR and MA processes, as well as the model denoted as ARIMA (P,D,Q)(BP,BD,BQ)(P,D,Q)(BP,BD,BQ), are consistent with those in 'JDemetra+'.

The available predefined 'JDemetra+' X13 and TRAMO-SEATS model specifications are described in the tables below:

X13:

Identifier | Log/level detection | Outliers detection | Calendar effects | ARIMA
RG0 | NA | NA | NA | Airline(+mean)
RG1 | automatic | AO/LS/TC | NA | Airline(+mean)
RG2c | automatic | AO/LS/TC | 2 td vars + Easter | Airline(+mean)
RG3 | automatic | AO/LS/TC | NA | automatic
RG4c | automatic | AO/LS/TC | 2 td vars + Easter | automatic
RG5c | automatic | AO/LS/TC | 7 td vars + Easter | automatic

TRAMO-SEATS:

Identifier | Log/level detection | Outliers detection | Calendar effects | ARIMA
TR0 | NA | NA | NA | Airline(+mean)
TR1 | automatic | AO/LS/TC | NA | Airline(+mean)
TR2 | automatic | AO/LS/TC | 2 td vars + Easter | Airline(+mean)
TR3 | automatic | AO/LS/TC | NA | automatic
TR4 | automatic | AO/LS/TC | 2 td vars + Easter | automatic
TR5 | automatic | AO/LS/TC | 7 td vars + Easter | automatic
TRfull | automatic | AO/LS/TC | automatic | automatic

Value

The jregarima/jregarima_x13/jregarima_tramoseats functions return a jSA object that contains the result of the pre-adjustment method without any formatting. Therefore, the computation is faster than with the regarima/regarima_x13/regarima_tramoseats functions. The results of the seasonal adjustment can be extracted with the function get_indicators.

The regarima/regarima_x13/regarima_tramoseats functions return an object of class "regarima" and sub-class "X13" or "TRAMO_SEATS". regarima_x13 returns an object of class c("regarima","X13") and regarima_tramoseats, an object of class c("regarima","TRAMO_SEATS"). For the function regarima, the sub-class of the object depends on the used method that is defined by the spec object class.

An object of class "regarima" is a list containing the following components:

specification

a list with the model specification as defined by the spec argument. See also the Value of the regarima_spec_x13 and regarima_spec_tramoseats functions.

arma

a vector containing the orders of the autoregressive (AR), moving average (MA), seasonal AR and seasonal MA processes, as well as the regular and seasonal differencing orders (P,D,Q) (BP,BD,BQ).

arima.coefficients

a matrix containing the estimated regular and seasonal AR and MA coefficients, as well as the associated standard errors and t-statistics values. The estimated coefficients can be also extracted with the function coef (whose output also includes the regression coefficients).

regression.coefficients

a matrix containing the estimated regression variables (i.e.: mean, calendar effect, outliers and user-defined regressors) coefficients, as well as the associated standard errors and t-statistics values. The estimated coefficients can be also extracted with the function coef (whose output also includes the arima coefficients).

loglik

a matrix containing the log-likelihood of the RegARIMA model as well as the associated model selection criteria statistics (AIC, AICC, BIC and BICC) and parameters (np = number of parameters in the likelihood, neffectiveobs = number of effective observations in the likelihood). These statistics can also be extracted with the function logLik.

model

a list containing information on the model specification after its estimation (spec_rslt), as well as the decomposed elements of the input series (ts matrix, effects). The model specification includes information on the estimation method (Model) and time span (T.span), whether the original series was log transformed (Log transformation) and details on the regression part of the RegARIMA model i.e. if it includes a Mean, Trading days effects (if so, it provides the number of regressors), Leap year effect, Easter effect and whether outliers were detected (Outliers (if so, it provides the number of outliers). The decomposed elements of the input series contain the linearised series (y_lin) and the deterministic components i.e.: trading days effect (tde), Easter effect (ee), other moving holidays effect (omhe) and outliers effect (total - out, related to irregular - out_i, related to trend - out_t, related to seasonal - out_s).

residuals

the residuals (time series). They can be also extracted with the function residuals.

residuals.stat

a list containing statistics on the RegARIMA residuals. It provides the residuals standard error (st.error) and the results of normality, independence and linearity of the residuals (tests) - object of class c("regarima_rtests","data.frame").

forecast

a ts matrix containing the forecast of the original series (fcst) and its standard error (fcsterr).

References

More information and examples related to 'JDemetra+' features in the online documentation: https://jdemetra-new-documentation.netlify.app/

BOX G.E.P. and JENKINS G.M. (1970), "Time Series Analysis: Forecasting and Control", Holden-Day, San Francisco.

BOX G.E.P., JENKINS G.M., REINSEL G.C. and LJUNG G.M. (2015), "Time Series Analysis: Forecasting and Control", John Wiley & Sons, Hoboken, N. J., 5th edition.

Examples

# X13 method
myseries <- ipi_c_eu[, "FR"]
myreg <- regarima_x13(myseries, spec ="RG5c")
summary(myreg)
plot(myreg)

myspec1 <- regarima_spec_x13(myreg, tradingdays.option = "WorkingDays")
myreg1 <- regarima(myseries, myspec1)

myspec2 <- regarima_spec_x13(myreg, usrdef.outliersEnabled = TRUE,
             usrdef.outliersType = c("LS", "AO"),
             usrdef.outliersDate = c("2008-10-01", "2002-01-01"),
             usrdef.outliersCoef = c(36, 14),
             transform.function = "None")
myreg2 <- regarima(myseries, myspec2)
myreg2

myspec3 <- regarima_spec_x13(myreg, automdl.enabled = FALSE,
             arima.p = 1, arima.q = 1,
             arima.bp = 0, arima.bq = 1,
             arima.coefEnabled = TRUE,
             arima.coef = c(-0.8, -0.6, 0),
             arima.coefType = c(rep("Fixed", 2), "Undefined"))
s_arimaCoef(myspec3)
myreg3 <- regarima(myseries, myspec3)
summary(myreg3)
plot(myreg3)

 # TRAMO-SEATS method
myspec <- regarima_spec_tramoseats("TRfull")
myreg <- regarima(myseries, myspec)
myreg

myspec2 <- regarima_spec_tramoseats(myspec, tradingdays.mauto = "Unused",
             tradingdays.option = "WorkingDays",
             easter.type = "Standard",
             automdl.enabled = FALSE, arima.mu = TRUE)
myreg2 <- regarima(myseries, myspec2)

var1 <- ts(rnorm(length(myseries))*10, start = start(myseries), frequency = 12)
var2 <- ts(rnorm(length(myseries))*100, start = start(myseries), frequency = 12)
var <- ts.union(var1, var2)
myspec3 <- regarima_spec_tramoseats(myspec,
             usrdef.varEnabled = TRUE, usrdef.var = var)
s_preVar(myspec3)
myreg3 <- regarima(myseries, myspec3)
myreg3

RegARIMA model specification, pre-adjustment in TRAMO-SEATS

Description

Function to create (and/or modify) a c("regarima_spec","TRAMO_SEATS") class object with the RegARIMA model specification for the TRAMO-SEATS method. The object can be created from the name (character) of a predefined 'JDemetra+' model specification, a previous specification (c("regarima_spec","TRAMO_SEATS") object) or a TRAMO-SEATS RegARIMA model (c("regarima","TRAMO_SEATS")).

Usage

regarima_spec_tramoseats(
  spec = c("TRfull", "TR0", "TR1", "TR2", "TR3", "TR4", "TR5"),
  preliminary.check = NA,
  estimate.from = NA_character_,
  estimate.to = NA_character_,
  estimate.first = NA_integer_,
  estimate.last = NA_integer_,
  estimate.exclFirst = NA_integer_,
  estimate.exclLast = NA_integer_,
  estimate.tol = NA_integer_,
  estimate.eml = NA,
  estimate.urfinal = NA_integer_,
  transform.function = c(NA, "Auto", "None", "Log"),
  transform.fct = NA_integer_,
  usrdef.outliersEnabled = NA,
  usrdef.outliersType = NA,
  usrdef.outliersDate = NA,
  usrdef.outliersCoef = NA,
  usrdef.varEnabled = NA,
  usrdef.var = NA,
  usrdef.varType = NA,
  usrdef.varCoef = NA,
  tradingdays.mauto = c(NA, "Unused", "FTest", "WaldTest"),
  tradingdays.pftd = NA_integer_,
  tradingdays.option = c(NA, "TradingDays", "WorkingDays", "UserDefined", "None"),
  tradingdays.leapyear = NA,
  tradingdays.stocktd = NA_integer_,
  tradingdays.test = c(NA, "Separate_T", "Joint_F", "None"),
  easter.type = c(NA, "Unused", "Standard", "IncludeEaster", "IncludeEasterMonday"),
  easter.julian = NA,
  easter.duration = NA_integer_,
  easter.test = NA,
  outlier.enabled = NA,
  outlier.from = NA_character_,
  outlier.to = NA_character_,
  outlier.first = NA_integer_,
  outlier.last = NA_integer_,
  outlier.exclFirst = NA_integer_,
  outlier.exclLast = NA_integer_,
  outlier.ao = NA,
  outlier.tc = NA,
  outlier.ls = NA,
  outlier.so = NA,
  outlier.usedefcv = NA,
  outlier.cv = NA_integer_,
  outlier.eml = NA,
  outlier.tcrate = NA_integer_,
  automdl.enabled = NA,
  automdl.acceptdefault = NA,
  automdl.cancel = NA_integer_,
  automdl.ub1 = NA_integer_,
  automdl.ub2 = NA_integer_,
  automdl.armalimit = NA_integer_,
  automdl.reducecv = NA_integer_,
  automdl.ljungboxlimit = NA_integer_,
  automdl.compare = NA,
  arima.mu = NA,
  arima.p = NA_integer_,
  arima.d = NA_integer_,
  arima.q = NA_integer_,
  arima.bp = NA_integer_,
  arima.bd = NA_integer_,
  arima.bq = NA_integer_,
  arima.coefEnabled = NA,
  arima.coef = NA,
  arima.coefType = NA,
  fcst.horizon = NA_integer_
)

Arguments

spec

the model specification. It can be the name (character) of a predefined 'JDemetra+' model specification (see Details), an object of class c("regarima_spec","TRAMO_SEATS") or an object of class c("regarima", "TRAMO_SEATS"). The default is "TRfull".

preliminary.check

a logical to check the quality of the input series and exclude highly problematic series e.g. the series with a number of identical observations and/or missing values above pre-specified threshold values.

The time span of the series, which is the (sub)period used to estimate the regarima model, is controlled by the following six variables: estimate.from, estimate.to, estimate.first, estimate.last, estimate.exclFirst and estimate.exclLast; where estimate.from and estimate.to have priority over the remaining span control variables, estimate.last and estimate.first have priority over estimate.exclFirst and estimate.exclLast, and estimate.last has priority over estimate.first. Default= "All".

estimate.from

a character in format "YYYY-MM-DD" indicating the start of the time span (e.g. "1900-01-01"). It can be combined with the parameter estimate.to.

estimate.to

a character in format "YYYY-MM-DD" indicating the end of the time span (e.g. "2020-12-31"). It can be combined with the parameter estimate.from.

estimate.first

numeric, the number of periods considered at the beginning of the series.

estimate.last

numeric, the number of periods considered at the end of the series.

estimate.exclFirst

numeric, the number of periods excluded at the beginning of the series. It can be combined with the parameter estimate.exclLast.

estimate.exclLast

numeric, the number of periods excluded at the end of the series. It can be combined with the parameter estimate.exclFirst.

estimate.tol

numeric, the convergence tolerance. The absolute changes in the log-likelihood function are compared to this value to check for the convergence of the estimation iterations.

estimate.eml

logical, the exact maximum likelihood estimation. If TRUE, the program performs an exact maximum likelihood estimation. If FASLE, the Unconditional Least Squares method is used.

estimate.urfinal

numeric, the final unit root limit. The threshold value for the final unit root test for identification of differencing orders. If the magnitude of an AR root for the final model is smaller than this number, then a unit root is assumed, the order of the AR polynomial is reduced by one and the appropriate order of the differencing (non-seasonal, seasonal) is increased.

transform.function

the transformation of the input series: "None" = no transformation of the series; "Log" = takes the log of the series; "Auto" = the program tests for the log-level specification.

transform.fct

numeric controlling the bias in the log/level pre-test: transform.fct > 1 favours levels, transform.fct< 1 favours logs. Considered only when transform.function is set to "Auto".

Control variables for the pre-specified outliers. Said pre-specified outliers are used in the model only when enabled (usrdef.outliersEnabled=TRUE) and when the outliers' type (usrdef.outliersType) and date (usrdef.outliersDate) are provided.

usrdef.outliersEnabled

logical. If TRUE, the program uses the pre-specified outliers.

usrdef.outliersType

a vector defining the outliers' type. Possible types are: ("AO") = additive, ("LS") = level shift, ("TC") = transitory change, ("SO") = seasonal outlier. E.g.: usrdef.outliersType= c("AO","AO","LS").

usrdef.outliersDate

a vector defining the outliers' date. The dates should be characters in format "YYYY-MM-DD". E.g.: usrdef.outliersDate= c("2009-10-01","2005-02-01","2003-04-01").

usrdef.outliersCoef

a vector providing fixed coefficients for the outliers. The coefficients can't be fixed if the parameter transform.function is set to "Auto" (i.e. if the series transformation needs to be pre-defined.) E.g.: usrdef.outliersCoef= c(200,170,20).

Control variables for the user-defined variables:

usrdef.varEnabled

logical If TRUE, the program uses the user-defined variables.

usrdef.var

a time series (ts) or a matrix of time series (mts) containing the user-defined variables.

usrdef.varType

a vector of character(s) defining the user-defined variables component type. Possible types are: "Undefined", "Series", "Trend", "Seasonal", "SeasonallyAdjusted", "Irregular", "Calendar". To use the user-defined calendar regressors, the type "Calendar" must be defined in conjunction with tradingdays.option = "UserDefined". Otherwise, the program will automatically set usrdef.varType = "Undefined".

usrdef.varCoef

a vector providing fixed coefficients for the user-defined variables. The coefficients can't be fixed if transform.function is set to "Auto" (i.e. if the series transformation needs to be pre-defined).

tradingdays.mauto

defines whether the calendar effects should be added to the model manually ("Unused") or automatically. During the automatic selection, the choice of the number of calendar variables can be based on the F-Test ("FTest") or the Wald Test ("WaldTest"); the model with higher F value is chosen, provided that it is higher than tradingdays.pftd).

tradingdays.pftd

numeric. The p-value used in the test specified by the automatic parameter (tradingdays.mauto) to assess the significance of the pre-tested calendar effects variables and whether they should be included in the RegArima model.

Control variables for the manual selection of calendar effects variables (tradingdays.mauto is set to "Unused"):

tradingdays.option

to choose the trading days regression variables: "TradingDays" = six day-of-the-week regression variables; "WorkingDays" = one working/non-working day contrast variable; "None" = no correction for trading days and working days effects; "UserDefined" = user-defined trading days regressors (regressors must be defined by the usrdef.var argument with usrdef.varType set to "Calendar" and usrdef.varEnabled = TRUE). "None" must also be chosen for the "day-of-week effects" correction (and tradingdays.stocktd must be modified accordingly).

tradingdays.leapyear

logical. Specifies if the leap-year correction should be included. If TRUE, the model includes the leap-year effect.

tradingdays.stocktd

numeric indicating the day of the month when inventories and other stock are reported (to denote the last day of the month set the variable to 31). Modifications of this variable are taken into account only when tradingdays.option is set to "None".

tradingdays.test

defines the pre-tests of the trading day effects: "None" = calendar variables are used in the model without pre-testing; "Separate_T" = a t-test is applied to each trading day variable separately and the trading day variables are included in the RegArima model if at least one t-statistic is greater than 2.6 or if two t-statistics are greater than 2.0 (in absolute terms); "Joint_F" = a joint F-test of significance of all the trading day variables. The trading day effect is significant if the F statistic is greater than 0.95.

easter.type

acharacter that specifies the presence and the length of the Easter effect: "Unused" = the Easter effect is not considered; "Standard" = influences the period of n days strictly before Easter Sunday; "IncludeEaster" = influences the entire period (n) up to and including Easter Sunday; "IncludeEasterMonday" = influences the entire period (n) up to and including Easter Monday.

easter.julian

logical. If TRUE, the program uses the Julian Easter (expressed in Gregorian calendar).

easter.duration

numeric indicating the duration of the Easter effect (length in days, between 1 and 15).

easter.test

logical. If TRUE, the program performs a t-test for the significance of the Easter effect. The Easter effect is considered as significant if the modulus of t-statistic is greater than 1.96.

outlier.enabled

logical. If TRUE, the automatic detection of outliers is enabled in the defined time span.

The time span of the series to be searched for outliers is controlled by the following six variables: outlier.from, outlier.to, outlier.first, outlier.last, outlier.exclFirst and outlier.exclLast; where outlier.from and outlier.to have priority over the remaining span control variables, outlier.last and outlier.first have priority over outlier.exclFirst and outlier.exclLast, and outlier.last has priority over outlier.first.

outlier.from

a character in format "YYYY-MM-DD" indicating the start of the time span (e.g. "1900-01-01"). It can be combined with outlier.to.

outlier.to

a character in format "YYYY-MM-DD" indicating the end of the time span (e.g. "2020-12-31"). It can be combined with outlier.from.

outlier.first

numeric specifying the number of periods considered at the beginning of the series.

outlier.last

numeric specifying the number of periods considered at the end of the series.

outlier.exclFirst

numeric specifying the number of periods excluded at the beginning of the series. It can be combined with outlier.exclLast.

outlier.exclLast

numeric specifying the number of periods excluded at the end of the series. It can be combined with outlier.exclFirst.

outlier.ao

logical. If TRUE, the automatic detection of additive outliers is enabled (outlier.enabled must also be set to TRUE).

outlier.tc

logical. If TRUE, the automatic detection of transitory changes is enabled (outlier.enabled must also be set to TRUE).

outlier.ls

logical. If TRUE, the automatic detection of level shifts is enabled (outlier.enabled must also be set to TRUE).

outlier.so

logical. If TRUE, the automatic detection of seasonal outliers is enabled (outlier.enabled must also be set to TRUE).

outlier.usedefcv

logical. If TRUE, the critical value for the outliers' detection procedure is automatically determined by the number of observations in the outlier detection time span. If FALSE, the procedure uses the entered critical value (outlier.cv).

outlier.cv

numeric. The entered critical value for the outliers' detection procedure. The modification of this variable is only taken in to account when outlier.usedefcv is set to FALSE.

outlier.eml

logical for the exact likelihood estimation method. It controls the method applied for a parameter estimation in the intermediate steps of the automatic detection and correction of outliers. If TRUE, an exact likelihood estimation method is used. When FALSE, the fast Hannan-Rissanen method is used.

outlier.tcrate

numeric. The rate of decay for the transitory change outlier.

automdl.enabled

logical. If TRUE, the automatic modelling of the ARIMA model is enabled. If FALSE, the parameters of the ARIMA model can be specified.

Control variables for the automatic modelling of the ARIMA model (automdl.enabled is set to TRUE):

automdl.acceptdefault

logical. If TRUE, the default model (ARIMA(0,1,1)(0,1,1)) may be chosen in the first step of the automatic model identification. If the Ljung-Box Q statistics for the residuals is acceptable, the default model is accepted and no further attempt will be made to identify another model.

automdl.cancel

numeric, the cancellation limit. If the difference in moduli of an AR and an MA roots (when estimating ARIMA(1,0,1)(1,0,1) models in the second step of the automatic identification of the differencing orders) is smaller than the cancellation limit, the two roots are assumed equal and canceled out.

automdl.ub1

numeric, the first unit root limit. It is the threshold value for the initial unit root test in the automatic differencing procedure. When one of the roots in the estimation of the ARIMA(2,0,0)(1,0,0) plus mean model, performed in the first step of the automatic model identification procedure, is larger than first unit root limit in modulus, it is set equal to unity.

automdl.ub2

numeric, the second unit root limit. When one of the roots in the estimation of the ARIMA(1,0,1)(1,0,1) plus mean model, which is performed in the second step of the automatic model identification procedure, is larger than second unit root limit in modulus, it is checked if there is a common factor in the corresponding AR and MA polynomials of the ARMA model that can be canceled (see automdl.cancel). If there is no cancellation, the AR root is set equal to unity (i.e. the differencing order changes).

automdl.armalimit

numeric, the arma limit. It is the threshold value for t-statistics of ARMA coefficients and the constant term used for the final test of model parsimony. If the highest order ARMA coefficient has a t-value smaller than this value in magnitude, the order of the model is reduced. If the constant term has a t-value smaller than the ARMA limit in magnitude, it is removed from the set of regressors.

automdl.reducecv

numeric, ReduceCV. The percentage by which the outlier critical value will be reduced when an identified model is found to have a Ljung-Box statistic with an unacceptable confidence coefficient. The parameter should be between 0 and 1, and will only be active when automatic outlier identification is enabled. The reduced critical value will be set to (1-ReduceCV)xCV, where CV is the original critical value.

automdl.ljungboxlimit

numeric, the Ljung Box limit, setting the acceptance criterion for the confidence intervals of the Ljung-Box Q statistic. If the LjungBox Q statistics for the residuals of a final model is greater than Ljung Box limit, then the model is rejected, the outlier critical value is reduced, and model and outlier identification (if specified) is redone with a reduced value.

automdl.compare

logical. If TRUE, the program compares the model identified by the automatic procedure to the default model (ARIMA(0,1,1)(0,1,1)) and the model with the best fit is selected. Criteria considered are residual diagnostics, the model structure and the number of outliers.

Control variables for the non-automatic modelling of the ARIMA model (automdl.enabled is set to FALSE):

arima.mu

logical. If TRUE, the mean is considered as part of the ARIMA model.

arima.p

numeric. The order of the non-seasonal autoregressive (AR) polynomial.

arima.d

numeric. The regular differencing order.

arima.q

numeric. The order of the non-seasonal moving average (MA) polynomial.

arima.bp

numeric. The order of the seasonal autoregressive (AR) polynomial.

arima.bd

numeric. The seasonal differencing order.

arima.bq

numeric. The order of the seasonal moving average (MA) polynomial.

Control variables for the user-defined ARMA coefficients. Such coefficients can be defined for the regular and seasonal autoregressive (AR) polynomials and moving average (MA) polynomials. The model considers the coefficients only if the procedure for their estimation (arima.coefType) is provided, and the number of provided coefficients matches the sum of (regular and seasonal) AR and MA orders (p,q,bp,bq).

arima.coefEnabled

logical. If TRUE, the program uses the user-defined ARMA coefficients.

arima.coef

a vector providing the coefficients for the regular and seasonal AR and MA polynomials. The length of the vector must be equal to the sum of the regular and seasonal AR and MA orders. The coefficients shall be provided in the following order: regular AR (Phi - p elements), regular MA (Theta - q elements), seasonal AR (BPhi - bp elements) and seasonal MA (BTheta - bq elements). E.g.: arima.coef=c(0.6,0.7) with arima.p=1, arima.q=0,arima.bp=1 and arima.bq=0.

arima.coefType

avector defining the ARMA coefficients estimation procedure. Possible procedures are: "Undefined" = no use of user-defined input (i.e. coefficients are estimated), "Fixed" = fixes the coefficients at the value provided by the user, "Initial" = the value defined by the user is used as initial condition. For orders for which the coefficients shall not be defined, the arima.coef can be set to NA or 0 or the arima.coefType can be set to "Undefined". E.g.: arima.coef = c(-0.8,-0.6,NA), arima.coefType = c("Fixed","Fixed","Undefined").

fcst.horizon

numeric, the forecasting horizon. The length of the forecasts generated by the RegARIMA model in periods (positive values) or years (negative values). By default, the program generates two years forecasts (fcst.horizon set to -2).

Details

The available predefined 'JDemetra+' model specifications are described in the table below:

Identifier | Log/level detection | Outliers detection | Calendar effects | ARIMA
TR0 | NA | NA | NA | Airline(+mean)
TR1 | automatic | AO/LS/TC | NA | Airline(+mean)
TR2 | automatic | AO/LS/TC | 2 td vars + Easter | Airline(+mean)
TR3 | automatic | AO/LS/TC | NA | automatic
TR4 | automatic | AO/LS/TC | 2 td vars + Easter | automatic
TR5 | automatic | AO/LS/TC | 7 td vars + Easter | automatic
TRfull | automatic | AO/LS/TC | automatic | automatic

Value

A list of class c("regarima_spec","TRAMO_SEATS") with the following components, each referring to a different part of the RegARIMA model specification, mirroring the arguments of the function (for details, see the arguments description). Each lowest-level component (except the span, pre-specified outliers, user-defined variables and pre-specified ARMA coefficients) is structured within a data frame with columns denoting different variables of the model specification and rows referring to: first row = the base specification, as provided within the argument spec; second row = user modifications as specified by the remaining arguments of the function (e.g.: arima.d); and third row = the final model specification, values that will be used in the function regarima. The final specification (third row) shall include user modifications (row two) unless they were wrongly specified. The pre-specified outliers, user-defined variables and pre-specified ARMA coefficients consist of a list with the Predefined (base model specification) and Final values.

estimate

a data frame containing Variables referring to: span - time span to be used for the estimation, tolerance - argument estimate.tol, exact_ml - argument estimate.eml, urfinal - argument esimate.urfinal. The final values can be also accessed with the function s_estimate.

transform

a data frame containing variables referring to: tfunction - argument transform.function, fct - argument transform.fct. The final values can be also accessed with the function s_transform.

regression

a list containing information on the user-defined variables (userdef), trading.days effect and easter effect. The user-defined part includes: specification - data frame with the information if pre-specified outliers (outlier) and user-defined variables (variables) are included in the model and if fixed coefficients are used (outlier.coef and variables.coef). The final values can be also accessed with the function s_usrdef; outliers - matrixes with the outliers (Predefined and Final). The final outliers can be also accessed with the function s_preOut; and variables - list with the Predefined and Final user-defined variables (series) and its description (description) including information on the variable type and values of fixed coefficients. The final user-defined variables can be also accessed with the function s_preVar.

The trading.days data frame variables refer to: automatic - argument tradingdays.mauto, pftd - argument tradingdays.pftd, option - argument tradingdays.option, leapyear - argument tradingdays.leapyear, stocktd - argument tradingdays.stocktd, test - argument tradingdays.test. The final trading.days values can be also accessed with the function s_td. The easter data frame variables refer to: type - argument easter.type, julian - argument easter.julian, duration - argument easter.duration, test - argument easter.test. The final easter values can be also accessed with the function s_easter.

outliers

a data frame. Variables referring to: ao - argument outlier.ao, tc - argument outlier.tc, ls - argument outlier.ls, so - argument outlier.so, usedefcv - argument outlier.usedefcv, cv - argument outlier.cv, eml - argument outlier.eml, tcrate - argument outlier.tcrate. The final values can be also accessed with the function s_out.

arima

a list containing a data frame with the ARIMA settings (specification) and matrices giving information on the pre-specified ARMA coefficients (coefficients). The matrix Predefined refers to the pre-defined model specification and matrix Final, to the final specification. Both matrices contain the values of the ARMA coefficients and the procedure for its estimation. In the data frame specification, the variable enabled refers to the argument automdl.enabled and all remaining variables (automdl.acceptdefault, automdl.cancel, automdl.ub1, automdl.ub2, automdl.armalimit, automdl.reducecv, automdl.ljungboxlimit, automdl.compare, arima.mu, arima.p, arima.d, arima.q, arima.bp, arima.bd, arima.bq), to the respective function arguments. The final values of the specification can be also accessed with the function s_arima, and final pre-specified ARMA coefficients with the function s_arimaCoef.

forecast

a data frame with the forecasting horizon (argument fcst.horizon). The final value can be also accessed with the function s_fcst.

span

a matrix containing the final time span for the model estimation and outliers' detection. It contains the same information as the variable span in the data frames estimate and outliers. The matrix can be also accessed with the function s_span.

References

More information and examples related to 'JDemetra+' features in the online documentation: https://jdemetra-new-documentation.netlify.app/

Examples

myseries <- ipi_c_eu[, "FR"]
myspec1 <- regarima_spec_tramoseats(spec = "TRfull")
myreg1 <- regarima(myseries, spec = myspec1)

 # To modify a pre-specified model specification
myspec2 <- regarima_spec_tramoseats(spec = "TRfull",
             tradingdays.mauto = "Unused",
             tradingdays.option = "WorkingDays",
             easter.type = "Standard",
             automdl.enabled = FALSE, arima.mu = TRUE)
myreg2 <- regarima(myseries, spec = myspec2)

 # To modify the model specification of a "regarima" object
myspec3 <- regarima_spec_tramoseats(myreg1,
             tradingdays.mauto = "Unused",
             tradingdays.option = "WorkingDays",
             easter.type = "Standard", automdl.enabled = FALSE,
             arima.mu = TRUE)
myreg3 <- regarima(myseries, myspec3)

 # To modify the model specification of a "regarima_spec" object
myspec4 <- regarima_spec_tramoseats(myspec1,
             tradingdays.mauto = "Unused",
             tradingdays.option = "WorkingDays",
             easter.type = "Standard",
             automdl.enabled = FALSE, arima.mu = TRUE)
myreg4 <- regarima(myseries, myspec4)

 # Pre-specified outliers
myspec1 <- regarima_spec_tramoseats(spec = "TRfull",
             usrdef.outliersEnabled = TRUE,
             usrdef.outliersType = c("LS", "LS"),
             usrdef.outliersDate = c("2008-10-01" ,"2003-01-01"),
             usrdef.outliersCoef = c(10, -8), transform.function = "None")
s_preOut(myspec1)
myreg1 <- regarima(myseries, myspec1)
myreg1
s_preOut(myreg1)


 # User-defined variables
var1 <- ts(rnorm(length(myseries))*10, start = start(myseries),
           frequency = 12)
var2 <- ts(rnorm(length(myseries))*100, start = start(myseries),
           frequency = 12)
var <- ts.union(var1, var2)

myspec1 <- regarima_spec_tramoseats(spec = "TRfull",
            usrdef.varEnabled = TRUE, usrdef.var = var)
s_preVar(myspec1)
myreg1 <- regarima(myseries,myspec1)

myspec2 <- regarima_spec_tramoseats(spec = "TRfull",
             usrdef.varEnabled = TRUE,
             usrdef.var = var, usrdef.varCoef = c(17,-1),
             transform.function = "None")
myreg2 <- regarima(myseries, myspec2)

 # Pre-specified ARMA coefficients
myspec1 <- regarima_spec_tramoseats(spec = "TRfull",
             arima.coefEnabled = TRUE, automdl.enabled = FALSE,
             arima.p = 2, arima.q = 0, arima.bp = 1, arima.bq = 1,
             arima.coef = c(-0.12, -0.12, -0.3, -0.99),
             arima.coefType = rep("Fixed", 4))
myreg1 <- regarima(myseries, myspec1)
myreg1
summary(myreg1)
s_arimaCoef(myspec1)
s_arimaCoef(myreg1)

RegARIMA model specification: the pre-adjustment in X13

Description

Function to create (and/or modify) a c("regarima_spec","X13") class object with the RegARIMA model specification for the X13 method. The object can be created from a predefined 'JDemetra+' model specification (a character), a previous specification (c("regarima_spec","X13") object) or a X13 RegARIMA model (c("regarima","X13")).

Usage

regarima_spec_x13(
  spec = c("RG5c", "RG0", "RG1", "RG2c", "RG3", "RG4c"),
  preliminary.check = NA,
  estimate.from = NA_character_,
  estimate.to = NA_character_,
  estimate.first = NA_integer_,
  estimate.last = NA_integer_,
  estimate.exclFirst = NA_integer_,
  estimate.exclLast = NA_integer_,
  estimate.tol = NA_integer_,
  transform.function = c(NA, "Auto", "None", "Log"),
  transform.adjust = c(NA, "None", "LeapYear", "LengthOfPeriod"),
  transform.aicdiff = NA_integer_,
  usrdef.outliersEnabled = NA,
  usrdef.outliersType = NA,
  usrdef.outliersDate = NA,
  usrdef.outliersCoef = NA,
  usrdef.varEnabled = NA,
  usrdef.var = NA,
  usrdef.varType = NA,
  usrdef.varCoef = NA,
  tradingdays.option = c(NA, "TradingDays", "WorkingDays", "UserDefined", "None"),
  tradingdays.autoadjust = NA,
  tradingdays.leapyear = c(NA, "LeapYear", "LengthOfPeriod", "None"),
  tradingdays.stocktd = NA_integer_,
  tradingdays.test = c(NA, "Remove", "Add", "None"),
  easter.enabled = NA,
  easter.julian = NA,
  easter.duration = NA_integer_,
  easter.test = c(NA, "Add", "Remove", "None"),
  outlier.enabled = NA,
  outlier.from = NA_character_,
  outlier.to = NA_character_,
  outlier.first = NA_integer_,
  outlier.last = NA_integer_,
  outlier.exclFirst = NA_integer_,
  outlier.exclLast = NA_integer_,
  outlier.ao = NA,
  outlier.tc = NA,
  outlier.ls = NA,
  outlier.so = NA,
  outlier.usedefcv = NA,
  outlier.cv = NA_integer_,
  outlier.method = c(NA, "AddOne", "AddAll"),
  outlier.tcrate = NA_integer_,
  automdl.enabled = NA,
  automdl.acceptdefault = NA,
  automdl.cancel = NA_integer_,
  automdl.ub1 = NA_integer_,
  automdl.ub2 = NA_integer_,
  automdl.mixed = NA,
  automdl.balanced = NA,
  automdl.armalimit = NA_integer_,
  automdl.reducecv = NA_integer_,
  automdl.ljungboxlimit = NA_integer_,
  automdl.ubfinal = NA_integer_,
  arima.mu = NA,
  arima.p = NA_integer_,
  arima.d = NA_integer_,
  arima.q = NA_integer_,
  arima.bp = NA_integer_,
  arima.bd = NA_integer_,
  arima.bq = NA_integer_,
  arima.coefEnabled = NA,
  arima.coef = NA,
  arima.coefType = NA,
  fcst.horizon = NA_integer_
)

Arguments

spec

the model specification. It can be the name (character) of a pre-defined 'JDemetra+' model specification (see Details), an object of class c("regarima_spec","X13") or an object of class c("regarima", "X13"). The default value is "RG5c".

preliminary.check

a Boolean to check the quality of the input series and exclude highly problematic ones (e.g. the series with a number of identical observations and/or missing values above pre-specified threshold values).

The time span of the series, which is the (sub)period used to estimate the regarima model, is controlled by the following six variables: estimate.from, estimate.to, estimate.first, estimate.last, estimate.exclFirst and estimate.exclLast; where estimate.from and estimate.to have priority over the remaining span control variables, estimate.last and estimate.first have priority over estimate.exclFirst and estimate.exclLast, and estimate.last has priority over estimate.first. Default= "All".

estimate.from

a character in format "YYYY-MM-DD" indicating the start of the time span (e.g. "1900-01-01"). It can be combined with the parameter estimate.to.

estimate.to

a character in format "YYYY-MM-DD" indicating the end of the time span (e.g. "2020-12-31"). It can be combined with the parameter estimate.from.

estimate.first

a numeric specifying the number of periods considered at the beginning of the series.

estimate.last

numeric specifying the number of periods considered at the end of the series.

estimate.exclFirst

a numeric specifying the number of periods excluded at the beginning of the series. It can be combined with the parameter estimate.exclLast.

estimate.exclLast

a numeric specifying the number of periods excluded at the end of the series. It can be combined with the parameter estimate.exclFirst.

estimate.tol

a numeric, convergence tolerance. The absolute changes in the log-likelihood function are compared to this value to check for the convergence of the estimation iterations.

transform.function

the transformation of the input series: "None" = no transformation of the series; "Log" = takes the log of the series; "Auto" = the program tests for the log-level specification.

transform.adjust

pre-adjustment of the input series for the length of period or leap year effects: "None" = no adjustment; "LeapYear" = leap year effect; "LengthOfPeriod" = length of period. Modifications of this variable are taken into account only when transform.function is set to "Log".

transform.aicdiff

a numeric defining the difference in AICC needed to accept no transformation when the automatic transformation selection is chosen (considered only when transform.function is set to "Auto").

Control variables for the pre-specified outliers. The pre-specified outliers are used in the model only when enabled (usrdef.outliersEnabled=TRUE) and the outlier type (usrdef.outliersType) and date (usrdef.outliersDate) are provided.

usrdef.outliersEnabled

logical. If TRUE, the program uses the pre-specified outliers.

usrdef.outliersType

a vector defining the outlier type. Possible types are: ("AO") = additive, ("LS") = level shift, ("TC") = transitory change, ("SO") = seasonal outlier. E.g.: usrdef.outliersType = c("AO","AO","LS").

usrdef.outliersDate

a vector defining the outlier dates. The dates should be characters in format "YYYY-MM-DD". E.g.: usrdef.outliersDate= c("2009-10-01","2005-02-01","2003-04-01").

usrdef.outliersCoef

a vector providing fixed coefficients for the outliers. The coefficients can't be fixed if transform.function is set to "Auto" i.e. the series transformation need to be pre-defined. E.g.: usrdef.outliersCoef=c(200,170,20).

Control variables for the user-defined variables:

usrdef.varEnabled

a logical. If TRUE, the program uses the user-defined variables.

usrdef.var

a time series (ts) or a matrix of time series (mts) with the user-defined variables.

usrdef.varType

a vector of character(s) defining the user-defined variables component type. Possible types are: "Undefined", "Series", "Trend", "Seasonal", "SeasonallyAdjusted", "Irregular", "Calendar". The type "Calendar"must be used with tradingdays.option = "UserDefined" to use user-defined calendar regressors. If not specified, the program will assign the "Undefined" type.

usrdef.varCoef

a vector providing fixed coefficients for the user-defined variables. The coefficients can't be fixed if transform.function is set to "Auto" i.e. the series transformation need to be pre-defined.

tradingdays.option

to specify the set of trading days regression variables: "TradingDays" = six day-of-the-week regression variables; "WorkingDays" = one working/non-working day contrast variable; "None" = no correction for trading days and working days effects; "UserDefined" = user-defined trading days regressors (regressors must be defined by the usrdef.var argument with usrdef.varType set to "Calendar" and usrdef.varEnabled = TRUE). "None" must also be specified for the "day-of-week effects" correction (tradingdays.stocktd to be modified accordingly).

tradingdays.autoadjust

a logical. If TRUE, the program corrects automatically for the leap year effect. Modifications of this variable are taken into account only when transform.function is set to "Auto".

tradingdays.leapyear

a character to specify whether or not to include the leap-year effect in the model: "LeapYear" = leap year effect; "LengthOfPeriod" = length of period, "None" = no effect included. The leap-year effect can be pre-specified in the model only if the input series hasn't been pre-adjusted (transform.adjust set to "None") and if the automatic correction for the leap-year effect isn't selected (tradingdays.autoadjust set to FALSE).

tradingdays.stocktd

a numeric indicating the day of the month when inventories and other stock are reported (to denote the last day of the month, set the variable to 31). Modifications of this variable are taken into account only when tradingdays.option is set to "None".

tradingdays.test

defines the pre-tests for the significance of the trading day regression variables based on the AICC statistics: "Add" = the trading day variables are not included in the initial regression model but can be added to the RegARIMA model after the test; "Remove" = the trading day variables belong to the initial regression model but can be removed from the RegARIMA model after the test; "None" = the trading day variables are not pre-tested and are included in the model.

easter.enabled

a logical. If TRUE, the program considers the Easter effect in the model.

easter.julian

a logical. If TRUE, the program uses the Julian Easter (expressed in Gregorian calendar).

easter.duration

a numeric indicating the duration of the Easter effect (length in days, between 1 and 20).

easter.test

defines the pre-tests for the significance of the Easter effect based on the t-statistic (the Easter effect is considered as significant if the t-statistic is greater than 1.96): "Add" = the Easter effect variable is not included in the initial regression model but can be added to the RegARIMA model after the test; "Remove" = the Easter effect variable belongs to the initial regression model but can be removed from the RegARIMA model after the test; "None" = the Easter effect variable is not pre-tested and is included in the model.

outlier.enabled

a logical. If TRUE, the automatic detection of outliers is enabled in the defined time span.

The time span during which outliers will be searched is controlled by the following six variables: outlier.from, outlier.to, outlier.first, outlier.last, outlier.exclFirst and outlier.exclLast; where outlier.from and outlier.to have priority over the remaining span control variables, outlier.last and outlier.first have priority over outlier.exclFirst and outlier.exclLast, and outlier.last has priority over outlier.first.

outlier.from

a character in format "YYYY-MM-DD" indicating the start of the time span (e.g. "1900-01-01"). It can be combined with the parameter outlier.to.

outlier.to

a character in format "YYYY-MM-DD" indicating the end of the time span (e.g. "2020-12-31"). it can be combined with the parameter outlier.from.

outlier.first

a numeric specifying the number of periods considered at the beginning of the series.

outlier.last

a numeric specifying the number of periods considered at the end of the series.

outlier.exclFirst

a numeric specifying the number of periods excluded at the beginning of the series. It can be combined with the parameter outlier.exclLast.

outlier.exclLast

a numeric specifying the number of periods excluded at the end of the series. It can be combined with the parameter outlier.exclFirst.

outlier.ao

a logical. If TRUE, the automatic detection of additive outliers is enabled (outlier.enabled must be also set to TRUE).

outlier.tc

a logical. If TRUE, the automatic detection of transitory changes is enabled (outlier.enabled must be also set to TRUE).

outlier.ls

a logical. If TRUE, the automatic detection of level shifts is enabled (outlier.enabled must be also set to TRUE).

outlier.so

a logical. If TRUE, the automatic detection of seasonal outliers is enabled (outlier.enabled must be also set to TRUE).

outlier.usedefcv

a logical. If TRUE, the critical value for the outlier detection procedure is automatically determined by the number of observations in the outlier detection time span. If FALSE, the procedure uses the entered critical value (outlier.cv).

outlier.cv

a numeric. The entered critical value for the outlier detection procedure. The modification of this variable is only taken into account when outlier.usedefcv is set to FALSE.

outlier.method

determines how the program successively adds detected outliers to the model. At present, only the AddOne method is supported.

outlier.tcrate

a numeric. The rate of decay for the transitory change outlier.

automdl.enabled

a logical. If TRUE, the automatic modelling of the ARIMA model is enabled. If FALSE, the parameters of the ARIMA model can be specified.

Control variables for the automatic modelling of the ARIMA model (when automdl.enabled is set to TRUE):

automdl.acceptdefault

a logical. If TRUE, the default model (ARIMA(0,1,1)(0,1,1)) may be chosen in the first step of the automatic model identification. If the Ljung-Box Q statistics for the residuals is acceptable, the default model is accepted and no further attempt will be made to identify another model.

automdl.cancel

the cancellation limit (numeric). If the difference in moduli of an AR and an MA roots (when estimating ARIMA(1,0,1)(1,0,1) models in the second step of the automatic identification of the differencing orders) is smaller than the cancellation limit, the two roots are assumed equal and cancel out.

automdl.ub1

the first unit root limit (numeric). It is the threshold value for the initial unit root test in the automatic differencing procedure. When one of the roots in the estimation of the ARIMA(2,0,0)(1,0,0) plus mean model, performed in the first step of the automatic model identification procedure, is larger than the first unit root limit in modulus, it is set equal to unity.

automdl.ub2

the second unit root limit (numeric). When one of the roots in the estimation of the ARIMA(1,0,1)(1,0,1) plus mean model, which is performed in the second step of the automatic model identification procedure, is larger than second unit root limit in modulus, it is checked if there is a common factor in the corresponding AR and MA polynomials of the ARMA model that can be canceled (see automdl.cancel). If there is no cancellation, the AR root is set equal to unity (i.e. the differencing order changes).

automdl.mixed

a logical. This variable controls whether ARIMA models with non-seasonal AR and MA terms or seasonal AR and MA terms will be considered in the automatic model identification procedure. If FALSE, a model with AR and MA terms in both the seasonal and non-seasonal parts of the model can be acceptable, provided there are no AR or MA terms in either the seasonal or non-seasonal terms.

automdl.balanced

a logical. If TRUE, the automatic model identification procedure will have a preference for balanced models (i.e. models for which the order of the combined AR and differencing operator is equal to the order of the combined MA operator).

automdl.armalimit

the ARMA limit (numeric). It is the threshold value for t-statistics of ARMA coefficients and constant term used for the final test of model parsimony. If the highest order ARMA coefficient has a t-value smaller than this value in magnitude, the order of the model is reduced. If the constant term t-value is smaller than the ARMA limit in magnitude, it is removed from the set of regressors.

automdl.reducecv

numeric, ReduceCV. The percentage by which the outlier's critical value will be reduced when an identified model is found to have a Ljung-Box statistic with an unacceptable confidence coefficient. The parameter should be between 0 and 1, and will only be active when automatic outlier identification is enabled. The reduced critical value will be set to (1-ReduceCV)*CV, where CV is the original critical value.

automdl.ljungboxlimit

the Ljung Box limit (numeric). Acceptance criterion for the confidence intervals of the Ljung-Box Q statistic. If the LjungBox Q statistics for the residuals of a final model is greater than the Ljung Box limit, then the model is rejected, the outlier critical value is reduced and model and outlier identification (if specified) is redone with a reduced value.

automdl.ubfinal

numeric, final unit root limit. The threshold value for the final unit root test. If the magnitude of an AR root for the final model is smaller than the final unit root limit, then a unit root is assumed, the order of the AR polynomial is reduced by one and the appropriate order of the differencing (non-seasonal, seasonal) is increased. The parameter value should be greater than one.

Control variables for the non-automatic modelling of the ARIMA model (when automdl.enabled is set to FALSE):

arima.mu

logical. If TRUE, the mean is considered as part of the ARIMA model.

arima.p

numeric. The order of the non-seasonal autoregressive (AR) polynomial.

arima.d

numeric. The regular differencing order.

arima.q

numeric. The order of the non-seasonal moving average (MA) polynomial.

arima.bp

numeric. The order of the seasonal autoregressive (AR) polynomial.

arima.bd

numeric. The seasonal differencing order.

arima.bq

numeric. The order of the seasonal moving average (MA) polynomial.

Control variables for the user-defined ARMA coefficients. Coefficients can be defined for the regular and seasonal autoregressive (AR) polynomials and moving average (MA) polynomials. The model considers the coefficients only if the procedure for their estimation (arima.coefType) is provided, and the number of provided coefficients matches the sum of (regular and seasonal) AR and MA orders (p,q,bp,bq).

arima.coefEnabled

logical. If TRUE, the program uses the user-defined ARMA coefficients.

arima.coef

a vector providing the coefficients for the regular and seasonal AR and MA polynomials. The vector length must be equal to the sum of the regular and seasonal AR and MA orders. The coefficients shall be provided in the following order: regular AR (Phi; p elements), regular MA (Theta; q elements), seasonal AR (BPhi; bp elements) and seasonal MA (BTheta; bq elements). E.g.: arima.coef=c(0.6,0.7) with arima.p=1, arima.q=0,arima.bp=1 and arima.bq=0.

arima.coefType

a vector defining the ARMA coefficients estimation procedure. Possible procedures are: "Undefined" = no use of any user-defined input (i.e. coefficients are estimated), "Fixed" = the coefficients are fixed at the value provided by the user, "Initial" = the value defined by the user is used as the initial condition. For orders for which the coefficients shall not be defined, the arima.coef can be set to NA or 0, or the arima.coefType can be set to "Undefined". E.g.: arima.coef = c(-0.8,-0.6,NA), arima.coefType = c("Fixed","Fixed","Undefined").

fcst.horizon

the forecasting horizon (numeric). The forecast length generated by the RegARIMA model in periods (positive values) or years (negative values). By default, the program generates a two-year forecast (fcst.horizon set to -2).

Details

The available predefined 'JDemetra+' model specifications are described in the table below:

Identifier | Log/level detection | Outliers detection | Calendar effects | ARIMA
RG0 | NA | NA | NA | Airline(+mean)
RG1 | automatic | AO/LS/TC | NA | Airline(+mean)
RG2c | automatic | AO/LS/TC | 2 td vars + Easter | Airline(+mean)
RG3 | automatic | AO/LS/TC | NA | automatic
RG4c | automatic | AO/LS/TC | 2 td vars + Easter | automatic
RG5c | automatic | AO/LS/TC | 7 td vars + Easter | automatic

Value

A list of class c("regarima_spec","X13") with the following components, each referring to a different part of the RegARIMA model specification, mirroring the arguments of the function (for details, see the arguments description). Each lowest-level component (except span, pre-specified outliers, user-defined variables and pre-specified ARMA coefficients) is structured within a data frame with columns denoting different variables of the model specification and rows referring to: first row = base specification, as provided within the argument spec; second row = user modifications as specified by the remaining arguments of the function (e.g.: arima.d); and third row = final model specification, values that will be used in the function regarima. The final specification (third row) shall include user modifications (row two) unless they were wrongly specified. The pre-specified outliers, user-defined variables and pre-specified ARMA coefficients consist of a list of Predefined (base model specification) and Final values.

estimate

a data frame. Variables referring to: span - time span for the model estimation, tolerance - argument estimate.tol. The final values can also be accessed with the function s_estimate.

transform

a data frame. Variables referring to: tfunction - argument transform.function, adjust - argument transform.adjust, aicdiff - argument transform.aicdiff. The final values can also be accessed with the function s_transform.

regression

a list containing the information on the user-defined variables (userdef), trading.days effect and easter effect. The user-defined part includes: specification - data frame with the information if pre-specified outliers (outlier) and user-defined variables (variables) are included in the model and if fixed coefficients are used (outlier.coef and variables.coef). The final values can also be accessed with the function s_usrdef; outliers - matrices with the outliers (Predefined and Final). The final outliers can also be accessed with the function s_preOut; and variables - a list with the Predefined and Final user-defined variables (series) and its description (description) including the information on the variable type and the values of fixed coefficients. The final user-defined variables can also be accessed with the function s_preVar. Within the data frame trading.days, the variables refer to: option - argument tradingdays.option, autoadjust - argument tradingdays.autoadjust, leapyear - argument tradingdays.leapyear, stocktd - argument tradingdays.stocktd, test - argument tradingdays.test. The final trading.days values can be also accessed with the function s_td. Within the data frame easter variables refer to: enabled - argument easter.enabled, julian - argument easter.julian, duration - argument easter.duration, test - argument easter.test. The final easter values can be also accessed with the function s_easter.

outliers

a data frame. Variables referring to: enabled - argument outlier.enabled, span - time span for the outlier detection, ao - argument outlier.ao, tc - argument outlier.tc, ls - argument outlier.ls, so - argument outlier.so, usedefcv - argument outlier.usedefcv, cv - argument outlier.cv, method - argument outlier.method, tcrate - argument outlier.tcrate. The final values can also be accessed with the function s_out.

arima

a list of a data frame with the ARIMA settings (specification) and matrices with the information on the pre-specified ARMA coefficients (coefficients). The matrix Predefined refers to the pre-defined model specification, and the matrix Final to the final specification. Both matrices contain the value of the ARMA coefficients and the procedure for its estimation. In the data frame specification, the variable enabled refers to the argument automdl.enabled and all remaining variables (automdl.acceptdefault, automdl.cancel, automdl.ub1, automdl.ub2, automdl.mixed, automdl.balanced, automdl.armalimit, automdl.reducecv, automdl.ljungboxlimit, automdl.ubfinal, arima.mu, arima.p, arima.d, arima.q, arima.bp, arima.bd, arima.bq), to the respective function arguments. The final values of the specification can be also accessed with the function s_arima and the final pre-specified ARMA coefficients, with the function s_arimaCoef.

forecast

a data frame with the forecast horizon (argument fcst.horizon). The final value can also be accessed with the function s_fcst.

span

a matrix containing the final time span for the model estimation and outlier detection. It contains the same information as the variable span in the data frames estimate and outliers. The matrix can be also accessed with the function s_span.

References

More information and examples related to 'JDemetra+' features in the online documentation: https://jdemetra-new-documentation.netlify.app/

Examples

myseries <- ipi_c_eu[, "FR"]
myspec1 <- regarima_spec_x13(spec = "RG5c")
myreg1 <- regarima(myseries, spec = myspec1)

 # To modify a pre-specified model specification
myspec2 <- regarima_spec_x13(spec = "RG5c",
                             tradingdays.option = "WorkingDays")
myreg2 <- regarima(myseries, spec = myspec2)

 # To modify the model specification of a "regarima" object
myspec3 <- regarima_spec_x13(myreg1, tradingdays.option = "WorkingDays")
myreg3 <- regarima(myseries, myspec3)

 # To modify the model specification of a "regarima_spec" object
myspec4 <- regarima_spec_x13(myspec1, tradingdays.option = "WorkingDays")
myreg4 <- regarima(myseries, myspec4)

 # Pre-specified outliers
myspec1 <- regarima_spec_x13(spec = "RG5c", usrdef.outliersEnabled = TRUE,
              usrdef.outliersType = c("LS", "AO"),
              usrdef.outliersDate = c("2008-10-01", "2002-01-01"),
              usrdef.outliersCoef = c(36, 14),
              transform.function = "None")

myreg1 <- regarima(myseries, myspec1)
myreg1
s_preOut(myreg1)


 # User-defined variables
var1 <- ts(rnorm(length(myseries))*10, start = start(myseries),
           frequency = 12)
var2 <- ts(rnorm(length(myseries))*100, start = start(myseries),
           frequency = 12)
var <- ts.union(var1, var2)

myspec1 <- regarima_spec_x13(spec = "RG5c", usrdef.varEnabled = TRUE,
                             usrdef.var = var)
myreg1 <- regarima(myseries, myspec1)
myreg1

myspec2 <- regarima_spec_x13(spec = "RG5c", usrdef.varEnabled = TRUE,
                             usrdef.var = var1, usrdef.varCoef = 2,
                             transform.function = "None")
myreg2 <- regarima(myseries, myspec2)
s_preVar(myreg2)

 # Pre-specified ARMA coefficients
myspec1 <- regarima_spec_x13(spec = "RG5c", automdl.enabled =FALSE,
             arima.p = 1, arima.q = 1, arima.bp = 0, arima.bq = 1,
             arima.coefEnabled = TRUE, arima.coef = c(-0.8, -0.6, 0),
             arima.coefType = c(rep("Fixed", 2), "Undefined"))

s_arimaCoef(myspec1)
myreg1 <- regarima(myseries, myspec1)
myreg1

Saving and loading a model specification, SA and pre-adjustment in X13 and TRAMO-SEATS

Description

save_spec saves a SA or RegARIMA model specification. load_spec loads the previously saved model specification.

Usage

save_spec(object, file = file.path(tempdir(), "spec.RData"))

load_spec(file = "spec.RData")

Arguments

object

an object of one of the following classes: c("SA_spec","X13"), c("SA_spec","TRAMO_SEATS"), c("SA","X13"), c("SA","TRAMO_SEATS"), c("regarima_spec","X13"), c("regarima_spec","TRAMO_SEATS"), c("regarima","X13"), c("regarima","TRAMO_SEATS").

file

the (path and) name of the file where the model specification will be/has been saved.

Details

save_spec saves the final model specification of a "SA_spec", "SA", "regarima_spec" or "regarima" class object. load_spec loads the previously saved model specification. It creates a c("SA_spec","X13"), c("sA_spec","TRAMO_SEATS"), c("regarima_spec","X13") or c("regarima_spec","TRAMO_SEATS") class object, in line with the class of the previously saved model specification.

Value

load_spec returns an object of class "SA_spec" or "regarima_spec".

References

More information and examples related to 'JDemetra+' features in the online documentation: https://jdemetra-new-documentation.netlify.app/

Examples

myseries <- ipi_c_eu[, "FR"]
myreg1 <- regarima_x13(myseries, spec = "RG5c")
myspec2 <- regarima_spec_x13(myreg1, estimate.from = "2005-10-01", outlier.from = "2010-03-01")
myreg2 <- regarima(myseries, myspec2)

myreg3 <- regarima_tramoseats(myseries, spec = "TRfull")
myspec4 <-regarima_spec_tramoseats(myreg3, tradingdays.mauto = "Unused",
                                  tradingdays.option ="WorkingDays",
                                  easter.type = "Standard",
                                  automdl.enabled = FALSE, arima.mu = TRUE)
myreg4 <-regarima(myseries, myspec4)

myspec6 <- x13_spec("RSA5c")
mysa6 <- x13(myseries, myspec6)

myspec7 <- tramoseats_spec("RSAfull")
mysa7 <- tramoseats(myseries, myspec7)

dir <- tempdir()

 # To save the model specification of a c("regarima_spec","X13") class object
save_spec(myspec2, file.path(dir, "specx13.RData"))
 # To save the model specification of a c("regarima","X13") class object
save_spec(myreg2, file.path(dir,"regx13.RData"))
 # To save the model specification of a c("regarima_spec","TRAMO_SEATS") class object
save_spec(myspec4, file.path(dir,"specTS.RData"))
 # To save the model specification of a c("regarima","TRAMO_SEATS") class object
save_spec(myreg4, file.path(dir,"regTS.RData"))
 # To save the model of a c("SA_spec","X13") class object
save_spec(myspec6, file.path(dir,"specFullx13.RData"))
 # To save the model of a c("SA","X13") class object
save_spec(mysa6, file.path(dir,"sax13.RData"))
 # To save the model of a c("SA_spec","TRAMO_SEATS") class object
save_spec(myspec7, file.path(dir,"specFullTS.RData"))
 # To save the model of a c("SA","TRAMO_SEATS") class object
save_spec(mysa7, file.path(dir,"saTS.RData"))

 # To load a model specification:
myspec2a <- load_spec(file.path(dir,"specx13.RData"))
myspec2b <- load_spec(file.path(dir,"regx13.RData"))
myspec4a <- load_spec(file.path(dir,"specTS.RData"))
myspec4b <- load_spec(file.path(dir,"regTS.RData"))
myspec6a <- load_spec(file.path(dir,"specFullx13.RData"))
myspec6b <- load_spec(file.path(dir,"sax13.RData"))
myspec7a <- load_spec(file.path(dir,"specFullTS.RData"))
myspec7b <- load_spec(file.path(dir,"saTS.RData"))

# To use the re-loaded specifications and models:
regarima(myseries, myspec2a)
x13(myseries, myspec6a)
tramoseats(myseries, myspec7a)

regarima(myseries, myspec4a)
x13(myseries, myspec6b)
tramoseats(myseries, myspec7b)

Save a workspace

Description

Function to save a workspace object into a 'JDemetra+' workspace.

Usage

save_workspace(workspace, file)

Arguments

workspace

the workspace object to export

file

the path where to export the 'JDemetra+' workspace (.xml file). By default, if not specified, a dialog box opens.

Value

A boolean indicating whether the export is successful.

See Also

load_workspace

Examples

dir <- tempdir()
# Creation and export of an empty 'JDemetra+' workspace
wk <- new_workspace()
new_multiprocessing(wk, "sa1")
save_workspace(wk, file.path(dir, "workspace.xml"))

Access a model specification, a SA or a pre-adjustment model in X13 and TRAMO-SEATS

Description

The following functions enable the access to different parts of the final model specification, as included in the "SA", "regarima", "SA_spec" and "regarima_spec" S3 class objects.

Usage

s_estimate(object = NA)

s_transform(object = NA)

s_usrdef(object = NA)

s_preOut(object = NA)

s_preVar(object = NA)

s_td(object = NA)

s_easter(object = NA)

s_out(object = NA)

s_arima(object = NA)

s_arimaCoef(object = NA)

s_fcst(object = NA)

s_span(object = NA)

s_x11(object = NA)

s_benchmarking(object = NA)

s_seats(object = NA)

Arguments

object

an object of one of the following classes: c("SA","X13"), c("SA","TRAMO_SEATS"), c("SA_spec","X13"), c("SA_spec","TRAMO_SEATS"), c("regarima","X13"), c("regarima","TRAMO_SEATS"), c("regarima_spec","X13"), c("regarima_spec","TRAMO_SEATS").

Value

  • s_estimate returns a data.frame with the estimate variables

  • s_transform returns a data.frame with the transform variables

  • s_usrdef returns a data.frame with the user-defined regressors (outliers and variables) model specification, indicating if those variables are included in the model and if coefficients are pre-specified

  • s_preOut returns a data.frame with the pre-specified outliers

  • s_preVar returns a list with information on the user-defined variables, including: series - the time series and description - data.frame with the variable type and coefficients

  • s_td returns a data.frame with the trading.days variables

  • s_easter returns a data.frame with the easter variable

  • s_out returns a data.frame with the outliers detection variables

  • s_arima returns a data.frame with the arima variables

  • s_arimaCoef returns a data.frame with the user-specified ARMA coefficients

  • s_fcst returns a data.frame with the forecast horizon

  • s_span returns a data.frame with the span variables

  • s_x11 returns a data.frame with the x11 variables

  • s_seats returns a data.frame with the seats variables

References

More information and examples related to 'JDemetra+' features in the online documentation: https://jdemetra-new-documentation.netlify.app/

Examples

myseries <- ipi_c_eu[, "FR"]
myreg1 <- regarima_x13(myseries, spec = "RG5c")
myspec1 <- regarima_spec_x13(myreg1,
             estimate.from = "2005-10-01",
             outlier.from = "2010-03-01")

s_estimate(myreg1)
s_estimate(myspec1)

s_transform(myreg1)
s_transform(myspec1)

s_usrdef(myreg1)
s_usrdef(myspec1)

myspec2 <- regarima_spec_x13(myreg1, usrdef.outliersEnabled = TRUE,
             usrdef.outliersType = c("LS", "AO"),
             usrdef.outliersDate = c("2009-10-01", "2005-02-01"))
myreg2 <- regarima(myseries, myspec2)

s_preOut(myreg2)
s_preOut(myspec2)

var1 <- ts(rnorm(length(myseries))*10, start = start(myseries), frequency = 12)
var2 <- ts(rnorm(length(myseries))*100, start = start(myseries), frequency = 12)
var3 <- ts.union(var1, var2)
myspec3 <- regarima_spec_x13(spec = "RG5c",
                             usrdef.varEnabled = TRUE,
                             usrdef.var = var3)
myreg3 <- regarima(myseries, myspec3)

s_preVar(myspec3)
s_preVar(myreg3)

s_td(myreg1)
s_td(myspec1)

s_easter(myreg1)
s_easter(myspec1)

s_out(myreg1)
s_out(myspec1)

s_arima(myreg1)
s_arima(myspec1)

myspec4 <- regarima_spec_x13(myreg1, automdl.enabled = FALSE,
             arima.coefEnabled = TRUE,
             arima.p = 1,arima.q = 1, arima.bp = 1, arima.bq = 1,
             arima.coef = rep(0.2, 4),
             arima.coefType = rep("Initial", 4))
myreg4 <- regarima(myseries, myspec4)

s_arimaCoef(myreg4)
s_arimaCoef(myspec4)

s_fcst(myreg1)
s_fcst(myspec1)

s_span(myreg1)
s_span(myspec1)

myspec5 <- x13_spec(spec = "RSA5c", x11.seasonalComp = FALSE)
mysa5 <- x13(myseries, myspec5)

s_x11(mysa5)
s_x11(myspec5)

myspec6 <- tramoseats_spec(spec = "RSAfull", seats.approx = "Noisy")
mysa6 <- tramoseats(myseries, myspec6)

s_seats(mysa6)
s_seats(mysa6)

Seasonal Adjustment with TRAMO-SEATS

Description

Functions to estimate the seasonally adjusted series (sa) with the TRAMO-SEATS method. This is achieved by decomposing the time series (y) into the trend-cycle (t), the seasonal component (s) and the irregular component (i). Calendar-related movements can be corrected in the pre-treatment (TRAMO) step. tramoseats returns a preformatted result while jtramoseats returns the Java objects of the seasonal adjustment.

Usage

jtramoseats(
  series,
  spec = c("RSAfull", "RSA0", "RSA1", "RSA2", "RSA3", "RSA4", "RSA5"),
  userdefined = NULL
)

tramoseats(
  series,
  spec = c("RSAfull", "RSA0", "RSA1", "RSA2", "RSA3", "RSA4", "RSA5"),
  userdefined = NULL
)

Arguments

series

an univariate time series

spec

a TRAMO-SEATS model specification. It can be the name (character) of a pre-defined TRAMO-SEATS 'JDemetra+' model specification (see Details), or an object of class c("SA_spec","TRAMO_SEATS"). The default value is "RSAfull".

userdefined

a character vector containing the additional output variables (see user_defined_variables).

Details

The first step of a seasonal adjustment consists in pre-adjusting the time series with TRAMO. This is done by removing its deterministic effects (calendar and outliers), using a regression model with ARIMA noise (RegARIMA, see: regarima). In the second part, the pre-adjusted series is decomposed by the SEATS algorithm into the following components: trend-cycle (t), seasonal component (s) and irregular component (i). The decomposition can be: additive (y=t+s+iy = t + s + i) or multiplicative (y=tsiy = t * s * i, in the latter case pre-adjustment and decomposition are performed on (log(y)=log(t)+log(s)+log(i)log(y) = log(t) + log(s) + log(i)).

In the TRAMO-SEATS method, the second step - SEATS ("Signal Extraction in ARIMA Time Series") - performs an ARIMA-based decomposition of an observed time series into unobserved components. More information on this method at https://jdemetra-new-documentation.netlify.app/m-seats-decomposition.

The available predefined 'JDemetra+' TRAMO-SEATS model specifications are described in the table below:

Identifier | Log/level detection | Outliers detection | Calendar effects | ARIMA
RSA0 | NA | NA | NA | Airline(+mean)
RSA1 | automatic | AO/LS/TC | NA | Airline(+mean)
RSA2 | automatic | AO/LS/TC | 2 td vars + Easter | Airline(+mean)
RSA3 | automatic | AO/LS/TC | NA | automatic
RSA4 | automatic | AO/LS/TC | 2 td vars + Easter | automatic
RSA5 | automatic | AO/LS/TC | 7 td vars + Easter | automatic
RSAfull | automatic | AO/LS/TC | automatic | automatic

Value

jtramoseats returns a jSA object that contains the results of the seasonal adjustment without any formatting. Therefore, the computation is faster than with the function tramoseats. The results of the seasonal adjustment can be extracted with the function get_indicators.

tramoseats returns an object of class c("SA","TRAMO_SEATS"), that is, a list containing :

regarima

an object of class c("regarima","TRAMO_SEATS"). More info in the Value section of the function regarima.

decomposition

an object of class "decomposition_SEATS", that is a five-element list:

  • specification a list with the SEATS algorithm specification. See also the function tramoseats_spec.

  • mode the decomposition mode

  • model the SEATS model list: model, sa, trend, seasonal, transitory, irregular, each element being a matrix of estimated coefficients.

  • linearized the time series matrix (mts) with the stochastic series decomposition (input series y_lin, seasonally adjusted series sa_lin, trend t_lin, seasonal s_lin, irregular i_lin)

  • components the time series matrix (mts) with the decomposition components (input series y_cmp, seasonally adjusted series sa_cmp, trend t_cmp, seasonal component s_cmp, irregular i_cmp)

final

an object of class c("final","mts","ts","matrix"). The matrix contains the final results of the seasonal adjustment: the original time series (y)and its forecast (y_f), the trend (t) and its forecast (t_f), the seasonally adjusted series (sa) and its forecast (sa_f), the seasonal component (s)and its forecast (s_f), and the irregular component (i) and its forecast (i_f).

diagnostics

an object of class "diagnostics", that is a list containing three types of tests results:

  • variance_decomposition a data.frame with the tests results on the relative contribution of the components to the stationary portion of the variance in the original series, after the removal of the long term trend;

  • residuals_test a data.frame with the tests results of the presence of seasonality in the residuals (including the statistic test values, the corresponding p-values and the parameters description);

  • combined_test the combined tests for stable seasonality in the entire series. The format is a two-element list with: tests_for_stable_seasonality, a data.frame containing the tests results (including the statistic test value, its p-value and the parameters description), and combined_seasonality_test, the summary.

user_defined

an object of class "user_defined": a list containing the additional userdefined variables.

References

More information and examples related to 'JDemetra+' features in the online documentation: https://jdemetra-new-documentation.netlify.app/

BOX G.E.P. and JENKINS G.M. (1970), "Time Series Analysis: Forecasting and Control", Holden-Day, San Francisco.

BOX G.E.P., JENKINS G.M., REINSEL G.C. and LJUNG G.M. (2015), "Time Series Analysis: Forecasting and Control", John Wiley & Sons, Hoboken, N. J., 5th edition.

See Also

tramoseats_spec, x13

Examples

#Example 1
myseries <- ipi_c_eu[, "FR"]
myspec <- tramoseats_spec("RSAfull")
mysa <- tramoseats(myseries, myspec)
mysa

# Equivalent to:
mysa1 <- tramoseats(myseries, spec = "RSAfull")
mysa1

#Example 2
var1 <- ts(rnorm(length(myseries))*10, start = start(myseries), frequency = 12)
var2 <- ts(rnorm(length(myseries))*100, start = start(myseries), frequency = 12)
var <- ts.union(var1, var2)
myspec2 <- tramoseats_spec(myspec, tradingdays.mauto = "Unused",
                           tradingdays.option = "WorkingDays",
                           easter.type = "Standard",
                           automdl.enabled = FALSE, arima.mu = TRUE,
                           usrdef.varEnabled = TRUE, usrdef.var = var)
s_preVar(myspec2)
mysa2 <- tramoseats(myseries, myspec2,
                    userdefined = c("decomposition.sa_lin_f",
                                    "decomposition.sa_lin_e"))
mysa2
plot(mysa2)
plot(mysa2$regarima)
plot(mysa2$decomposition)

TRAMO-SEATS model specification

Description

Function to create (and/or modify) a c("SA_spec", "TRAMO_SEATS") class object with the SA model specification for the TRAMO-SEATS method. It can be done from a pre-defined 'JDemetra+' model specification (a character), a previous specification (c("SA_spec", "TRAMO_SEATS") object) or a seasonal adjustment model (c("SA", "TRAMO_SEATS") object).

Usage

tramoseats_spec(
  spec = c("RSAfull", "RSA0", "RSA1", "RSA2", "RSA3", "RSA4", "RSA5"),
  preliminary.check = NA,
  estimate.from = NA_character_,
  estimate.to = NA_character_,
  estimate.first = NA_integer_,
  estimate.last = NA_integer_,
  estimate.exclFirst = NA_integer_,
  estimate.exclLast = NA_integer_,
  estimate.tol = NA_integer_,
  estimate.eml = NA,
  estimate.urfinal = NA_integer_,
  transform.function = c(NA, "Auto", "None", "Log"),
  transform.fct = NA_integer_,
  usrdef.outliersEnabled = NA,
  usrdef.outliersType = NA,
  usrdef.outliersDate = NA,
  usrdef.outliersCoef = NA,
  usrdef.varEnabled = NA,
  usrdef.var = NA,
  usrdef.varType = NA,
  usrdef.varCoef = NA,
  tradingdays.mauto = c(NA, "Unused", "FTest", "WaldTest"),
  tradingdays.pftd = NA_integer_,
  tradingdays.option = c(NA, "TradingDays", "WorkingDays", "UserDefined", "None"),
  tradingdays.leapyear = NA,
  tradingdays.stocktd = NA_integer_,
  tradingdays.test = c(NA, "Separate_T", "Joint_F", "None"),
  easter.type = c(NA, "Unused", "Standard", "IncludeEaster", "IncludeEasterMonday"),
  easter.julian = NA,
  easter.duration = NA_integer_,
  easter.test = NA,
  outlier.enabled = NA,
  outlier.from = NA_character_,
  outlier.to = NA_character_,
  outlier.first = NA_integer_,
  outlier.last = NA_integer_,
  outlier.exclFirst = NA_integer_,
  outlier.exclLast = NA_integer_,
  outlier.ao = NA,
  outlier.tc = NA,
  outlier.ls = NA,
  outlier.so = NA,
  outlier.usedefcv = NA,
  outlier.cv = NA_integer_,
  outlier.eml = NA,
  outlier.tcrate = NA_integer_,
  automdl.enabled = NA,
  automdl.acceptdefault = NA,
  automdl.cancel = NA_integer_,
  automdl.ub1 = NA_integer_,
  automdl.ub2 = NA_integer_,
  automdl.armalimit = NA_integer_,
  automdl.reducecv = NA_integer_,
  automdl.ljungboxlimit = NA_integer_,
  automdl.compare = NA,
  arima.mu = NA,
  arima.p = NA_integer_,
  arima.d = NA_integer_,
  arima.q = NA_integer_,
  arima.bp = NA_integer_,
  arima.bd = NA_integer_,
  arima.bq = NA_integer_,
  arima.coefEnabled = NA,
  arima.coef = NA,
  arima.coefType = NA,
  fcst.horizon = NA_integer_,
  seats.predictionLength = NA_integer_,
  seats.approx = c(NA, "None", "Legacy", "Noisy"),
  seats.trendBoundary = NA_integer_,
  seats.seasdBoundary = NA_integer_,
  seats.seasdBoundary1 = NA_integer_,
  seats.seasTol = NA_integer_,
  seats.maBoundary = NA_integer_,
  seats.method = c(NA, "Burman", "KalmanSmoother", "McElroyMatrix"),
  benchmarking.enabled = NA,
  benchmarking.target = c(NA, "Original", "CalendarAdjusted"),
  benchmarking.useforecast = NA,
  benchmarking.rho = NA_real_,
  benchmarking.lambda = NA_real_
)

Arguments

spec

a TRAMO-SEATS model specification. It can be the 'JDemetra+' name (character) of a predefined TRAMO-SEATS model specification (see Details), an object of class c("SA_spec","TRAMO_SEATS") or an object of class c("SA", "TRAMO_SEATS"). The default is "RSAfull".

preliminary.check

a logical to check the quality of the input series and exclude highly problematic series e.g. the series with a number of identical observations and/or missing values above pre-specified threshold values.

The time span of the series, which is the (sub)period used to estimate the regarima model, is controlled by the following six variables: estimate.from, estimate.to, estimate.first, estimate.last, estimate.exclFirst and estimate.exclLast; where estimate.from and estimate.to have priority over the remaining span control variables, estimate.last and estimate.first have priority over estimate.exclFirst and estimate.exclLast, and estimate.last has priority over estimate.first. Default= "All".

estimate.from

a character in format "YYYY-MM-DD" indicating the start of the time span (e.g. "1900-01-01"). It can be combined with the parameter estimate.to.

estimate.to

a character in format "YYYY-MM-DD" indicating the end of the time span (e.g. "2020-12-31"). It can be combined with the parameter estimate.from.

estimate.first

numeric, the number of periods considered at the beginning of the series.

estimate.last

numeric, the number of periods considered at the end of the series.

estimate.exclFirst

numeric, the number of periods excluded at the beginning of the series. It can be combined with the parameter estimate.exclLast.

estimate.exclLast

numeric, the number of periods excluded at the end of the series. It can be combined with the parameter estimate.exclFirst.

estimate.tol

numeric, the convergence tolerance. The absolute changes in the log-likelihood function are compared to this value to check for the convergence of the estimation iterations.

estimate.eml

logical, the exact maximum likelihood estimation. If TRUE, the program performs an exact maximum likelihood estimation. If FASLE, the Unconditional Least Squares method is used.

estimate.urfinal

numeric, the final unit root limit. The threshold value for the final unit root test for identification of differencing orders. If the magnitude of an AR root for the final model is smaller than this number, then a unit root is assumed, the order of the AR polynomial is reduced by one and the appropriate order of the differencing (non-seasonal, seasonal) is increased.

transform.function

the transformation of the input series: "None" = no transformation of the series; "Log" = takes the log of the series; "Auto" = the program tests for the log-level specification.

transform.fct

numeric controlling the bias in the log/level pre-test: transform.fct > 1 favours levels, transform.fct< 1 favours logs. Considered only when transform.function is set to "Auto".

Control variables for the pre-specified outliers. Said pre-specified outliers are used in the model only when enabled (usrdef.outliersEnabled=TRUE) and when the outliers' type (usrdef.outliersType) and date (usrdef.outliersDate) are provided.

usrdef.outliersEnabled

logical. If TRUE, the program uses the pre-specified outliers.

usrdef.outliersType

a vector defining the outliers' type. Possible types are: ("AO") = additive, ("LS") = level shift, ("TC") = transitory change, ("SO") = seasonal outlier. E.g.: usrdef.outliersType= c("AO","AO","LS").

usrdef.outliersDate

a vector defining the outliers' date. The dates should be characters in format "YYYY-MM-DD". E.g.: usrdef.outliersDate= c("2009-10-01","2005-02-01","2003-04-01").

usrdef.outliersCoef

a vector providing fixed coefficients for the outliers. The coefficients can't be fixed if the parameter transform.function is set to "Auto" (i.e. if the series transformation needs to be pre-defined.) E.g.: usrdef.outliersCoef= c(200,170,20).

Control variables for the user-defined variables:

usrdef.varEnabled

logical If TRUE, the program uses the user-defined variables.

usrdef.var

a time series (ts) or a matrix of time series (mts) containing the user-defined variables.

usrdef.varType

a vector of character(s) defining the user-defined variables component type. Possible types are: "Undefined", "Series", "Trend", "Seasonal", "SeasonallyAdjusted", "Irregular", "Calendar". To use the user-defined calendar regressors, the type "Calendar" must be defined in conjunction with tradingdays.option = "UserDefined". Otherwise, the program will automatically set usrdef.varType = "Undefined".

usrdef.varCoef

a vector providing fixed coefficients for the user-defined variables. The coefficients can't be fixed if transform.function is set to "Auto" (i.e. if the series transformation needs to be pre-defined).

tradingdays.mauto

defines whether the calendar effects should be added to the model manually ("Unused") or automatically. During the automatic selection, the choice of the number of calendar variables can be based on the F-Test ("FTest") or the Wald Test ("WaldTest"); the model with higher F value is chosen, provided that it is higher than tradingdays.pftd).

tradingdays.pftd

numeric. The p-value used in the test specified by the automatic parameter (tradingdays.mauto) to assess the significance of the pre-tested calendar effects variables and whether they should be included in the RegArima model.

Control variables for the manual selection of calendar effects variables (tradingdays.mauto is set to "Unused"):

tradingdays.option

to choose the trading days regression variables: "TradingDays" = six day-of-the-week regression variables; "WorkingDays" = one working/non-working day contrast variable; "None" = no correction for trading days and working days effects; "UserDefined" = user-defined trading days regressors (regressors must be defined by the usrdef.var argument with usrdef.varType set to "Calendar" and usrdef.varEnabled = TRUE). "None" must also be chosen for the "day-of-week effects" correction (and tradingdays.stocktd must be modified accordingly).

tradingdays.leapyear

logical. Specifies if the leap-year correction should be included. If TRUE, the model includes the leap-year effect.

tradingdays.stocktd

numeric indicating the day of the month when inventories and other stock are reported (to denote the last day of the month set the variable to 31). Modifications of this variable are taken into account only when tradingdays.option is set to "None".

tradingdays.test

defines the pre-tests of the trading day effects: "None" = calendar variables are used in the model without pre-testing; "Separate_T" = a t-test is applied to each trading day variable separately and the trading day variables are included in the RegArima model if at least one t-statistic is greater than 2.6 or if two t-statistics are greater than 2.0 (in absolute terms); "Joint_F" = a joint F-test of significance of all the trading day variables. The trading day effect is significant if the F statistic is greater than 0.95.

easter.type

acharacter that specifies the presence and the length of the Easter effect: "Unused" = the Easter effect is not considered; "Standard" = influences the period of n days strictly before Easter Sunday; "IncludeEaster" = influences the entire period (n) up to and including Easter Sunday; "IncludeEasterMonday" = influences the entire period (n) up to and including Easter Monday.

easter.julian

logical. If TRUE, the program uses the Julian Easter (expressed in Gregorian calendar).

easter.duration

numeric indicating the duration of the Easter effect (length in days, between 1 and 15).

easter.test

logical. If TRUE, the program performs a t-test for the significance of the Easter effect. The Easter effect is considered as significant if the modulus of t-statistic is greater than 1.96.

outlier.enabled

logical. If TRUE, the automatic detection of outliers is enabled in the defined time span.

The time span of the series to be searched for outliers is controlled by the following six variables: outlier.from, outlier.to, outlier.first, outlier.last, outlier.exclFirst and outlier.exclLast; where outlier.from and outlier.to have priority over the remaining span control variables, outlier.last and outlier.first have priority over outlier.exclFirst and outlier.exclLast, and outlier.last has priority over outlier.first.

outlier.from

a character in format "YYYY-MM-DD" indicating the start of the time span (e.g. "1900-01-01"). It can be combined with outlier.to.

outlier.to

a character in format "YYYY-MM-DD" indicating the end of the time span (e.g. "2020-12-31"). It can be combined with outlier.from.

outlier.first

numeric specifying the number of periods considered at the beginning of the series.

outlier.last

numeric specifying the number of periods considered at the end of the series.

outlier.exclFirst

numeric specifying the number of periods excluded at the beginning of the series. It can be combined with outlier.exclLast.

outlier.exclLast

numeric specifying the number of periods excluded at the end of the series. It can be combined with outlier.exclFirst.

outlier.ao

logical. If TRUE, the automatic detection of additive outliers is enabled (outlier.enabled must also be set to TRUE).

outlier.tc

logical. If TRUE, the automatic detection of transitory changes is enabled (outlier.enabled must also be set to TRUE).

outlier.ls

logical. If TRUE, the automatic detection of level shifts is enabled (outlier.enabled must also be set to TRUE).

outlier.so

logical. If TRUE, the automatic detection of seasonal outliers is enabled (outlier.enabled must also be set to TRUE).

outlier.usedefcv

logical. If TRUE, the critical value for the outliers' detection procedure is automatically determined by the number of observations in the outlier detection time span. If FALSE, the procedure uses the entered critical value (outlier.cv).

outlier.cv

numeric. The entered critical value for the outliers' detection procedure. The modification of this variable is only taken in to account when outlier.usedefcv is set to FALSE.

outlier.eml

logical for the exact likelihood estimation method. It controls the method applied for a parameter estimation in the intermediate steps of the automatic detection and correction of outliers. If TRUE, an exact likelihood estimation method is used. When FALSE, the fast Hannan-Rissanen method is used.

outlier.tcrate

numeric. The rate of decay for the transitory change outlier.

automdl.enabled

logical. If TRUE, the automatic modelling of the ARIMA model is enabled. If FALSE, the parameters of the ARIMA model can be specified.

Control variables for the automatic modelling of the ARIMA model (automdl.enabled is set to TRUE):

automdl.acceptdefault

logical. If TRUE, the default model (ARIMA(0,1,1)(0,1,1)) may be chosen in the first step of the automatic model identification. If the Ljung-Box Q statistics for the residuals is acceptable, the default model is accepted and no further attempt will be made to identify another model.

automdl.cancel

numeric, the cancellation limit. If the difference in moduli of an AR and an MA roots (when estimating ARIMA(1,0,1)(1,0,1) models in the second step of the automatic identification of the differencing orders) is smaller than the cancellation limit, the two roots are assumed equal and canceled out.

automdl.ub1

numeric, the first unit root limit. It is the threshold value for the initial unit root test in the automatic differencing procedure. When one of the roots in the estimation of the ARIMA(2,0,0)(1,0,0) plus mean model, performed in the first step of the automatic model identification procedure, is larger than first unit root limit in modulus, it is set equal to unity.

automdl.ub2

numeric, the second unit root limit. When one of the roots in the estimation of the ARIMA(1,0,1)(1,0,1) plus mean model, which is performed in the second step of the automatic model identification procedure, is larger than second unit root limit in modulus, it is checked if there is a common factor in the corresponding AR and MA polynomials of the ARMA model that can be canceled (see automdl.cancel). If there is no cancellation, the AR root is set equal to unity (i.e. the differencing order changes).

automdl.armalimit

numeric, the arma limit. It is the threshold value for t-statistics of ARMA coefficients and the constant term used for the final test of model parsimony. If the highest order ARMA coefficient has a t-value smaller than this value in magnitude, the order of the model is reduced. If the constant term has a t-value smaller than the ARMA limit in magnitude, it is removed from the set of regressors.

automdl.reducecv

numeric, ReduceCV. The percentage by which the outlier critical value will be reduced when an identified model is found to have a Ljung-Box statistic with an unacceptable confidence coefficient. The parameter should be between 0 and 1, and will only be active when automatic outlier identification is enabled. The reduced critical value will be set to (1-ReduceCV)xCV, where CV is the original critical value.

automdl.ljungboxlimit

numeric, the Ljung Box limit, setting the acceptance criterion for the confidence intervals of the Ljung-Box Q statistic. If the LjungBox Q statistics for the residuals of a final model is greater than Ljung Box limit, then the model is rejected, the outlier critical value is reduced, and model and outlier identification (if specified) is redone with a reduced value.

automdl.compare

logical. If TRUE, the program compares the model identified by the automatic procedure to the default model (ARIMA(0,1,1)(0,1,1)) and the model with the best fit is selected. Criteria considered are residual diagnostics, the model structure and the number of outliers.

Control variables for the non-automatic modelling of the ARIMA model (automdl.enabled is set to FALSE):

arima.mu

logical. If TRUE, the mean is considered as part of the ARIMA model.

arima.p

numeric. The order of the non-seasonal autoregressive (AR) polynomial.

arima.d

numeric. The regular differencing order.

arima.q

numeric. The order of the non-seasonal moving average (MA) polynomial.

arima.bp

numeric. The order of the seasonal autoregressive (AR) polynomial.

arima.bd

numeric. The seasonal differencing order.

arima.bq

numeric. The order of the seasonal moving average (MA) polynomial.

Control variables for the user-defined ARMA coefficients. Such coefficients can be defined for the regular and seasonal autoregressive (AR) polynomials and moving average (MA) polynomials. The model considers the coefficients only if the procedure for their estimation (arima.coefType) is provided, and the number of provided coefficients matches the sum of (regular and seasonal) AR and MA orders (p,q,bp,bq).

arima.coefEnabled

logical. If TRUE, the program uses the user-defined ARMA coefficients.

arima.coef

a vector providing the coefficients for the regular and seasonal AR and MA polynomials. The length of the vector must be equal to the sum of the regular and seasonal AR and MA orders. The coefficients shall be provided in the following order: regular AR (Phi - p elements), regular MA (Theta - q elements), seasonal AR (BPhi - bp elements) and seasonal MA (BTheta - bq elements). E.g.: arima.coef=c(0.6,0.7) with arima.p=1, arima.q=0,arima.bp=1 and arima.bq=0.

arima.coefType

avector defining the ARMA coefficients estimation procedure. Possible procedures are: "Undefined" = no use of user-defined input (i.e. coefficients are estimated), "Fixed" = fixes the coefficients at the value provided by the user, "Initial" = the value defined by the user is used as initial condition. For orders for which the coefficients shall not be defined, the arima.coef can be set to NA or 0 or the arima.coefType can be set to "Undefined". E.g.: arima.coef = c(-0.8,-0.6,NA), arima.coefType = c("Fixed","Fixed","Undefined").

fcst.horizon

numeric, the forecasting horizon. The length of the forecasts generated by the RegARIMA model in periods (positive values) or years (negative values). By default, the program generates two years forecasts (fcst.horizon set to -2).

seats.predictionLength

integer: the number of forecasts used in the decomposition. Negative values correspond to number of years. Default=-1.

seats.approx

character: the approximation mode. When the ARIMA model estimated by TRAMO does not accept an admissible decomposition, SEATS: "None" - performs an approximation; "Legacy" - replaces the model with a decomposable one; "Noisy" - estimates a new model by adding a white noise to the non-admissible model estimated by TRAMO. Default="Legacy".

seats.trendBoundary

numeric: the trend boundary. The boundary beyond which an AR root is integrated in the trend component. If the modulus of the inverse real root is greater than the trend boundary, the AR root is integrated in the trend component. Below this value, the root is integrated in the transitory component. Possible values [0,1]. Default=0.5.

seats.seasdBoundary

numeric: the seasonal boundary. The boundary beyond which a negative AR root is integrated in the seasonal component. If the modulus of the inverse negative real root is greater (or equal) than Seasonal boundary, the AR root is integrated into the seasonal component. Otherwise the root is integrated into the trend or transitory component. Possible values [0,1]. Default=0.8.

seats.seasdBoundary1

numeric: the seasonal boundary (unique). The boundary beyond which a negative AR root is integrated in the seasonal component, when the root is the unique seasonal root. If the modulus of the inverse negative real root is greater (or equal) than Seasonal boundary, the AR root is integrated into the seasonal component. Otherwise the root is integrated into the trend or transitory component. Possible values [0,1]. Default=0.8.

seats.seasTol

numeric: the seasonal tolerance. The tolerance (measured in degrees) to allocate the AR non-real roots to the seasonal component (if the modulus of the inverse complex AR root is greater than the trend boundary and the frequency of this root differs from one of the seasonal frequencies by less than Seasonal tolerance) or the transitory component (otherwise). Possible values in [0,10]. Default value 2.

seats.maBoundary

numeric: the MA unit root boundary. When the modulus of an estimated MA root falls in the range (xl, 1), it is set to xl. Possible values [0.9,1]. Default=0.95.

seats.method

character: the estimation method for the unobserved components. The choice can be made from:

  • "Burman": the default value. May result in a significant underestimation of the components' standard deviation, as it may become numerically unstable when some roots of the MA polynomial are near 1;

  • "KalmanSmoother": it is not disturbed by the (quasi-) unit roots in MA;

  • "McElroyMatrix": it has the same stability issues as the Burman's algorithm.

benchmarking.enabled

logical: to enable benchmarking. If TRUE, the benchmarking is enabled.

benchmarking.target

character: the target of the benchmarking procedure, which can be the raw series ("Original") or the series the adjusted for calendar effects ("CalendarAdjusted").

benchmarking.useforecast

logical: If TRUE, the forecasts of the seasonally adjusted variable and of the target variable are used in the benchmarking computation so the benchmarking constrains is also applied to the forecasting period.

benchmarking.rho

numeric: the value of the AR(1) parameter (set between 0 and 1) in the function used for benchmarking.

benchmarking.lambda

numeric: a parameter used for benchmarking that relatesto to the weights in the regression equation. It is typically equal to 0, 1/2 or 1.

Details

The available predefined 'JDemetra+' model specifications are described in the table below:

Identifier | Log/level detection | Outliers detection | Calendar effects | ARIMA
RSA0 | NA | NA | NA | Airline(+mean)
RSA1 | automatic | AO/LS/TC | NA | Airline(+mean)
RSA2 | automatic | AO/LS/TC | 2 td vars + Easter | Airline(+mean)
RSA3 | automatic | AO/LS/TC | NA | automatic
RSA4 | automatic | AO/LS/TC | 2 td vars + Easter | automatic
RSA5 | automatic | AO/LS/TC | 7 td vars + Easter | automatic
RSAfull | automatic | AO/LS/TC | automatic | automatic

Value

A two-element list of class c("SA_spec", "TRAMO_SEATS"), containing: (1) an object of class c("regarima_spec", "TRAMO_SEATS") with the RegARIMA model specification, (2) an object of class c("seats_spec", "data.frame") with the SEATS algorithm specification. Each component refers to a different part of the SA model specification, mirroring the arguments of the function (for details see the function arguments in the description). Each lowest-level component (except span, pre-specified outliers, user-defined variables and pre-specified ARMA coefficients) is structured as a data frame with columns denoting different variables of the model specification and rows referring to:

  • first row: the base specification, as provided within the argument spec;

  • second row: user modifications as specified by the remaining arguments of the function (e.g.: arima.d);

  • and third row: the final model specification.

    The final specification (third row) shall include user modifications (row two) unless they were wrongly specified. The pre-specified outliers, user-defined variables and pre-specified ARMA coefficients consist of a list of Predefined (base model specification) and Final values.

  • regarima: an object of class c("regarima_spec", "TRAMO_SEATS"). See Value of the function regarima_spec_tramoseats.

  • seats: a data.frame of class c("seats_spec", "data.frame"), containing the seats variables in line with the names of the arguments variables. The final values can also be accessed with the function s_seats.

References

More information and examples related to 'JDemetra+' features in the online documentation: https://jdemetra-new-documentation.netlify.app/

See Also

tramoseats

Examples

myseries <- ipi_c_eu[, "FR"]
myspec1 <- tramoseats_spec(spec = c("RSAfull"))
mysa1 <- tramoseats(myseries, spec = myspec1)

# To modify a pre-specified model specification
myspec2 <- tramoseats_spec(spec = "RSAfull", tradingdays.mauto = "Unused",
                           tradingdays.option = "WorkingDays",
                           easter.type = "Standard",
                           automdl.enabled = FALSE, arima.mu = TRUE)
mysa2 <- tramoseats(myseries, spec = myspec2)

# To modify the model specification of a "SA" object
myspec3 <- tramoseats_spec(mysa1, tradingdays.mauto = "Unused",
                           tradingdays.option = "WorkingDays",
                           easter.type = "Standard", automdl.enabled = FALSE, arima.mu = TRUE)
mysa3 <- tramoseats(myseries, myspec3)

# To modify the model specification of a "SA_spec" object
myspec4 <- tramoseats_spec(myspec1, tradingdays.mauto = "Unused",
                           tradingdays.option = "WorkingDays",
                           easter.type = "Standard", automdl.enabled = FALSE, arima.mu = TRUE)
mysa4 <- tramoseats(myseries, myspec4)

# Pre-specified outliers
myspec5 <- tramoseats_spec(spec = "RSAfull",
                           usrdef.outliersEnabled = TRUE,
                           usrdef.outliersType = c("LS", "LS"),
                           usrdef.outliersDate = c("2008-10-01", "2003-01-01"),
                           usrdef.outliersCoef = c(10,-8), transform.function = "None")
s_preOut(myspec5)
mysa5 <- tramoseats(myseries, myspec5)
mysa5
s_preOut(mysa5)

# User-defined calendar regressors
var1 <- ts(rnorm(length(myseries))*10, start = start(myseries), frequency = 12)
var2 <- ts(rnorm(length(myseries))*100, start = start(myseries), frequency = 12)
var<- ts.union(var1, var2)

myspec6 <- tramoseats_spec(spec = "RSAfull", tradingdays.option = "UserDefined",
                           usrdef.varEnabled = TRUE, usrdef.var = var,
                           usrdef.varType = c("Calendar", "Calendar"))
s_preVar(myspec6)
mysa6 <- tramoseats(myseries, myspec6)

myspec7 <- tramoseats_spec(spec = "RSAfull", usrdef.varEnabled = TRUE,
                           usrdef.var = var, usrdef.varCoef = c(17,-1),
                           transform.function = "None")
mysa7 <- tramoseats(myseries, myspec7)

# Pre-specified ARMA coefficients
myspec8 <- tramoseats_spec(spec = "RSAfull",
                           arima.coefEnabled = TRUE, automdl.enabled = FALSE,
                           arima.p = 2, arima.q = 0,
                           arima.bp = 1, arima.bq = 1,
                           arima.coef = c(-0.12, -0.12, -0.3, -0.99),
                           arima.coefType = rep("Fixed", 4))
mysa8 <- tramoseats(myseries, myspec8)
mysa8
s_arimaCoef(myspec8)
s_arimaCoef(mysa8)

Display a list of all the available output objects (series, parameters, diagnostics)

Description

Function generating a comprehensive list of available output variables (series, parameters, diagnostics) from the estimation process with x13 and tramoseats. Some items are available in the default estimation output but the remainder can be added using the userdefined parameter.

Usage

user_defined_variables(sa_object = c("X13-ARIMA", "TRAMO-SEATS"))

Arguments

sa_object

a character: "X13-ARIMA" to retrieve the additional output variables available for the X13-ARIMA method and "TRAMO-SEATS" for the TRAMO-SEATS method.

Value

a vector containing the names of all the available output objects (series, diagnostics, parameters)

References

More information and examples related to 'JDemetra+' features in the online documentation: https://jdemetra-new-documentation.netlify.app/

Examples

y<- ipi_c_eu[, "FR"]
user_defined_variables("X13-ARIMA")
m <- x13(y,"RSA5c", userdefined=c("b20","ycal","residuals.kurtosis" ))
m$user_defined$b20
m$user_defined$ycal
m$user_defined$residuals.kurtosis
user_defined_variables("TRAMO-SEATS")
m <- tramoseats(y,"RSAfull", userdefined=c("ycal","variancedecomposition.seasonality"))
m$user_defined$ycal
m$user_defined$variancedecomposition.seasonality

Seasonal Adjustment with X13-ARIMA

Description

Functions to estimate the seasonally adjusted series (sa) with the X13-ARIMA method. This is achieved by decomposing the time series (y) into the trend-cycle (t), the seasonal component (s) and the irregular component (i). Calendar-related movements can be corrected in the pre-treatment (regarima) step. x13 returns a preformatted result while jx13 returns the Java objects resulting from the seasonal adjustment.

Usage

jx13(
  series,
  spec = c("RSA5c", "RSA0", "RSA1", "RSA2c", "RSA3", "RSA4c", "X11"),
  userdefined = NULL
)

x13(
  series,
  spec = c("RSA5c", "RSA0", "RSA1", "RSA2c", "RSA3", "RSA4c", "X11"),
  userdefined = NULL
)

Arguments

series

an univariate time series

spec

the x13 model specification. It can be the name (character) of a pre-defined X13 'JDemetra+' model specification (see Details) or of a specification created with the x13_spec function. The default value is "RSA5c".

userdefined

a character vector containing the additional output variables (see user_defined_variables).

Details

The first step of a seasonal adjustment consists in pre-adjusting the time series. This is done by removing its deterministic effects (calendar and outliers), using a regression model with ARIMA noise (RegARIMA, see: regarima). In the second part, the pre-adjusted series is decomposed by the X11 algorithm into the following components: trend-cycle (t), seasonal component (s) and irregular component (i). The decomposition can be: additive (y=t+s+iy = t + s + i) or multiplicative (y=tsiy = t * s * i). More information on the X11 algorithm at https://jdemetra-new-documentation.netlify.app/m-x11-decomposition.

The available pre-defined 'JDemetra+' X13 model specifications are described in the table below:

Identifier | Log/level detection | Outliers detection | Calendar effects | ARIMA
RSA0 | NA | NA | NA | Airline(+mean)
RSA1 | automatic | AO/LS/TC | NA | Airline(+mean)
RSA2c | automatic | AO/LS/TC | 2 td vars + Easter | Airline(+mean)
RSA3 | automatic | AO/LS/TC | NA | automatic
RSA4c | automatic | AO/LS/TC | 2 td vars + Easter | automatic
RSA5c | automatic | AO/LS/TC | 7 td vars + Easter | automatic
X11 | NA | NA | NA | NA

Value

jx13 returns the result of the seasonal adjustment in a Java (jSA) object, without any formatting. Therefore, the computation is faster than with the x13 function. The results of the seasonal adjustment can be extracted with the function get_indicators.

x13 returns an object of class c("SA","X13"), that is, a list containing the following components:

regarima

an object of class c("regarima","X13"). More info in the Value section of the function regarima.

decomposition

an object of class "decomposition_X11", that is a six-element list:

  • specification a list with the X11 algorithm specification. See also the function x13_spec.

  • mode the decomposition mode

  • mstats the matrix with the M statistics

  • si_ratio the time series matrix (mts) with the d8 and d10 series

  • s_filter the seasonal filters

  • t_filter the trend filter

final

an object of class c("final","mts","ts","matrix"). The matrix contains the final results of the seasonal adjustment: the original time series (y)and its forecast (y_f), the trend (t) and its forecast (t_f), the seasonally adjusted series (sa) and its forecast (sa_f), the seasonal component (s)and its forecast (s_f), and the irregular component (i) and its forecast (i_f).

diagnostics

an object of class "diagnostics", that is a list containing three types of tests results:

  • variance_decomposition a data.frame with the tests results on the relative contribution of the components to the stationary portion of the variance in the original series, after the removal of the long term trend;

  • residuals_test a data.frame with the tests results of the presence of seasonality in the residuals (including the statistic test values, the corresponding p-values and the parameters description);

  • combined_test the combined tests for stable seasonality in the entire series. The format is a two elements list with: tests_for_stable_seasonality, a data.frame containing the tests results (including the statistic test value, its p-value and the parameters description), and combined_seasonality_test, the summary.

user_defined

an object of class "user_defined": a list containing the additional userdefined variables.

References

More information and examples related to 'JDemetra+' features in the online documentation: https://jdemetra-new-documentation.netlify.app/

See Also

x13_spec, tramoseats

Examples

myseries <- ipi_c_eu[, "FR"]
mysa <- x13(myseries, spec = "RSA5c")

myspec1 <- x13_spec(mysa, tradingdays.option = "WorkingDays",
            usrdef.outliersEnabled = TRUE,
            usrdef.outliersType = c("LS","AO"),
            usrdef.outliersDate = c("2008-10-01", "2002-01-01"),
            usrdef.outliersCoef = c(36, 14),
            transform.function = "None")
mysa1 <- x13(myseries, myspec1)
mysa1
summary(mysa1$regarima)

myspec2 <- x13_spec(mysa, automdl.enabled =FALSE,
            arima.coefEnabled = TRUE,
            arima.p = 1, arima.q = 1, arima.bp = 0, arima.bq = 1,
            arima.coef = c(-0.8, -0.6, 0),
            arima.coefType = c(rep("Fixed", 2), "Undefined"))
s_arimaCoef(myspec2)
mysa2 <- x13(myseries, myspec2,
             userdefined = c("decomposition.d18", "decomposition.d19"))
mysa2
plot(mysa2)
plot(mysa2$regarima)
plot(mysa2$decomposition)

X-13ARIMA model specification, SA/X13

Description

Function to create (and/or modify) a c("SA_spec", "X13") class object with the SA model specification for the X13 method. It can be done from a pre-defined 'JDemetra+' model specification (a character), a previous specification (c("SA_spec", "X13") object) or a seasonal adjustment model (c("SA", "X13") object).

Usage

x13_spec(
  spec = c("RSA5c", "RSA0", "RSA1", "RSA2c", "RSA3", "RSA4c", "X11"),
  preliminary.check = NA,
  estimate.from = NA_character_,
  estimate.to = NA_character_,
  estimate.first = NA_integer_,
  estimate.last = NA_integer_,
  estimate.exclFirst = NA_integer_,
  estimate.exclLast = NA_integer_,
  estimate.tol = NA_integer_,
  transform.function = c(NA, "Auto", "None", "Log"),
  transform.adjust = c(NA, "None", "LeapYear", "LengthOfPeriod"),
  transform.aicdiff = NA_integer_,
  usrdef.outliersEnabled = NA,
  usrdef.outliersType = NA,
  usrdef.outliersDate = NA,
  usrdef.outliersCoef = NA,
  usrdef.varEnabled = NA,
  usrdef.var = NA,
  usrdef.varType = NA,
  usrdef.varCoef = NA,
  tradingdays.option = c(NA, "TradingDays", "WorkingDays", "UserDefined", "None"),
  tradingdays.autoadjust = NA,
  tradingdays.leapyear = c(NA, "LeapYear", "LengthOfPeriod", "None"),
  tradingdays.stocktd = NA_integer_,
  tradingdays.test = c(NA, "Remove", "Add", "None"),
  easter.enabled = NA,
  easter.julian = NA,
  easter.duration = NA_integer_,
  easter.test = c(NA, "Add", "Remove", "None"),
  outlier.enabled = NA,
  outlier.from = NA_character_,
  outlier.to = NA_character_,
  outlier.first = NA_integer_,
  outlier.last = NA_integer_,
  outlier.exclFirst = NA_integer_,
  outlier.exclLast = NA_integer_,
  outlier.ao = NA,
  outlier.tc = NA,
  outlier.ls = NA,
  outlier.so = NA,
  outlier.usedefcv = NA,
  outlier.cv = NA_integer_,
  outlier.method = c(NA, "AddOne", "AddAll"),
  outlier.tcrate = NA_integer_,
  automdl.enabled = NA,
  automdl.acceptdefault = NA,
  automdl.cancel = NA_integer_,
  automdl.ub1 = NA_integer_,
  automdl.ub2 = NA_integer_,
  automdl.mixed = NA,
  automdl.balanced = NA,
  automdl.armalimit = NA_integer_,
  automdl.reducecv = NA_integer_,
  automdl.ljungboxlimit = NA_integer_,
  automdl.ubfinal = NA_integer_,
  arima.mu = NA,
  arima.p = NA_integer_,
  arima.d = NA_integer_,
  arima.q = NA_integer_,
  arima.bp = NA_integer_,
  arima.bd = NA_integer_,
  arima.bq = NA_integer_,
  arima.coefEnabled = NA,
  arima.coef = NA,
  arima.coefType = NA,
  fcst.horizon = NA_integer_,
  x11.mode = c(NA, "Undefined", "Additive", "Multiplicative", "LogAdditive",
    "PseudoAdditive"),
  x11.seasonalComp = NA,
  x11.lsigma = NA_integer_,
  x11.usigma = NA_integer_,
  x11.trendAuto = NA,
  x11.trendma = NA_integer_,
  x11.seasonalma = NA_character_,
  x11.fcasts = NA_integer_,
  x11.bcasts = NA_integer_,
  x11.calendarSigma = NA,
  x11.sigmaVector = NA,
  x11.excludeFcasts = NA,
  benchmarking.enabled = NA,
  benchmarking.target = c(NA, "Original", "CalendarAdjusted"),
  benchmarking.useforecast = NA,
  benchmarking.rho = NA_real_,
  benchmarking.lambda = NA_real_
)

Arguments

spec

an x13 model specification. It can be the 'JDemetra+' name (character) of a predefined X13 'JDemetra+' model specification (see Details), an object of class c("SA_spec","X13") or an object of class c("SA", "X13"). The default is "RSA5c".

preliminary.check

a Boolean to check the quality of the input series and exclude highly problematic ones (e.g. the series with a number of identical observations and/or missing values above pre-specified threshold values).

The time span of the series, which is the (sub)period used to estimate the regarima model, is controlled by the following six variables: estimate.from, estimate.to, estimate.first, estimate.last, estimate.exclFirst and estimate.exclLast; where estimate.from and estimate.to have priority over the remaining span control variables, estimate.last and estimate.first have priority over estimate.exclFirst and estimate.exclLast, and estimate.last has priority over estimate.first. Default= "All".

estimate.from

a character in format "YYYY-MM-DD" indicating the start of the time span (e.g. "1900-01-01"). It can be combined with the parameter estimate.to.

estimate.to

a character in format "YYYY-MM-DD" indicating the end of the time span (e.g. "2020-12-31"). It can be combined with the parameter estimate.from.

estimate.first

a numeric specifying the number of periods considered at the beginning of the series.

estimate.last

numeric specifying the number of periods considered at the end of the series.

estimate.exclFirst

a numeric specifying the number of periods excluded at the beginning of the series. It can be combined with the parameter estimate.exclLast.

estimate.exclLast

a numeric specifying the number of periods excluded at the end of the series. It can be combined with the parameter estimate.exclFirst.

estimate.tol

a numeric, convergence tolerance. The absolute changes in the log-likelihood function are compared to this value to check for the convergence of the estimation iterations.

transform.function

the transformation of the input series: "None" = no transformation of the series; "Log" = takes the log of the series; "Auto" = the program tests for the log-level specification.

transform.adjust

pre-adjustment of the input series for the length of period or leap year effects: "None" = no adjustment; "LeapYear" = leap year effect; "LengthOfPeriod" = length of period. Modifications of this variable are taken into account only when transform.function is set to "Log".

transform.aicdiff

a numeric defining the difference in AICC needed to accept no transformation when the automatic transformation selection is chosen (considered only when transform.function is set to "Auto").

Control variables for the pre-specified outliers. The pre-specified outliers are used in the model only when enabled (usrdef.outliersEnabled=TRUE) and the outlier type (usrdef.outliersType) and date (usrdef.outliersDate) are provided.

usrdef.outliersEnabled

logical. If TRUE, the program uses the pre-specified outliers.

usrdef.outliersType

a vector defining the outlier type. Possible types are: ("AO") = additive, ("LS") = level shift, ("TC") = transitory change, ("SO") = seasonal outlier. E.g.: usrdef.outliersType = c("AO","AO","LS").

usrdef.outliersDate

a vector defining the outlier dates. The dates should be characters in format "YYYY-MM-DD". E.g.: usrdef.outliersDate= c("2009-10-01","2005-02-01","2003-04-01").

usrdef.outliersCoef

a vector providing fixed coefficients for the outliers. The coefficients can't be fixed if transform.function is set to "Auto" i.e. the series transformation need to be pre-defined. E.g.: usrdef.outliersCoef=c(200,170,20).

Control variables for the user-defined variables:

usrdef.varEnabled

a logical. If TRUE, the program uses the user-defined variables.

usrdef.var

a time series (ts) or a matrix of time series (mts) with the user-defined variables.

usrdef.varType

a vector of character(s) defining the user-defined variables component type. Possible types are: "Undefined", "Series", "Trend", "Seasonal", "SeasonallyAdjusted", "Irregular", "Calendar". The type "Calendar"must be used with tradingdays.option = "UserDefined" to use user-defined calendar regressors. If not specified, the program will assign the "Undefined" type.

usrdef.varCoef

a vector providing fixed coefficients for the user-defined variables. The coefficients can't be fixed if transform.function is set to "Auto" i.e. the series transformation need to be pre-defined.

tradingdays.option

to specify the set of trading days regression variables: "TradingDays" = six day-of-the-week regression variables; "WorkingDays" = one working/non-working day contrast variable; "None" = no correction for trading days and working days effects; "UserDefined" = user-defined trading days regressors (regressors must be defined by the usrdef.var argument with usrdef.varType set to "Calendar" and usrdef.varEnabled = TRUE). "None" must also be specified for the "day-of-week effects" correction (tradingdays.stocktd to be modified accordingly).

tradingdays.autoadjust

a logical. If TRUE, the program corrects automatically for the leap year effect. Modifications of this variable are taken into account only when transform.function is set to "Auto".

tradingdays.leapyear

a character to specify whether or not to include the leap-year effect in the model: "LeapYear" = leap year effect; "LengthOfPeriod" = length of period, "None" = no effect included. The leap-year effect can be pre-specified in the model only if the input series hasn't been pre-adjusted (transform.adjust set to "None") and if the automatic correction for the leap-year effect isn't selected (tradingdays.autoadjust set to FALSE).

tradingdays.stocktd

a numeric indicating the day of the month when inventories and other stock are reported (to denote the last day of the month, set the variable to 31). Modifications of this variable are taken into account only when tradingdays.option is set to "None".

tradingdays.test

defines the pre-tests for the significance of the trading day regression variables based on the AICC statistics: "Add" = the trading day variables are not included in the initial regression model but can be added to the RegARIMA model after the test; "Remove" = the trading day variables belong to the initial regression model but can be removed from the RegARIMA model after the test; "None" = the trading day variables are not pre-tested and are included in the model.

easter.enabled

a logical. If TRUE, the program considers the Easter effect in the model.

easter.julian

a logical. If TRUE, the program uses the Julian Easter (expressed in Gregorian calendar).

easter.duration

a numeric indicating the duration of the Easter effect (length in days, between 1 and 20).

easter.test

defines the pre-tests for the significance of the Easter effect based on the t-statistic (the Easter effect is considered as significant if the t-statistic is greater than 1.96): "Add" = the Easter effect variable is not included in the initial regression model but can be added to the RegARIMA model after the test; "Remove" = the Easter effect variable belongs to the initial regression model but can be removed from the RegARIMA model after the test; "None" = the Easter effect variable is not pre-tested and is included in the model.

outlier.enabled

a logical. If TRUE, the automatic detection of outliers is enabled in the defined time span.

The time span during which outliers will be searched is controlled by the following six variables: outlier.from, outlier.to, outlier.first, outlier.last, outlier.exclFirst and outlier.exclLast; where outlier.from and outlier.to have priority over the remaining span control variables, outlier.last and outlier.first have priority over outlier.exclFirst and outlier.exclLast, and outlier.last has priority over outlier.first.

outlier.from

a character in format "YYYY-MM-DD" indicating the start of the time span (e.g. "1900-01-01"). It can be combined with the parameter outlier.to.

outlier.to

a character in format "YYYY-MM-DD" indicating the end of the time span (e.g. "2020-12-31"). it can be combined with the parameter outlier.from.

outlier.first

a numeric specifying the number of periods considered at the beginning of the series.

outlier.last

a numeric specifying the number of periods considered at the end of the series.

outlier.exclFirst

a numeric specifying the number of periods excluded at the beginning of the series. It can be combined with the parameter outlier.exclLast.

outlier.exclLast

a numeric specifying the number of periods excluded at the end of the series. It can be combined with the parameter outlier.exclFirst.

outlier.ao

a logical. If TRUE, the automatic detection of additive outliers is enabled (outlier.enabled must be also set to TRUE).

outlier.tc

a logical. If TRUE, the automatic detection of transitory changes is enabled (outlier.enabled must be also set to TRUE).

outlier.ls

a logical. If TRUE, the automatic detection of level shifts is enabled (outlier.enabled must be also set to TRUE).

outlier.so

a logical. If TRUE, the automatic detection of seasonal outliers is enabled (outlier.enabled must be also set to TRUE).

outlier.usedefcv

a logical. If TRUE, the critical value for the outlier detection procedure is automatically determined by the number of observations in the outlier detection time span. If FALSE, the procedure uses the entered critical value (outlier.cv).

outlier.cv

a numeric. The entered critical value for the outlier detection procedure. The modification of this variable is only taken into account when outlier.usedefcv is set to FALSE.

outlier.method

determines how the program successively adds detected outliers to the model. At present, only the AddOne method is supported.

outlier.tcrate

a numeric. The rate of decay for the transitory change outlier.

automdl.enabled

a logical. If TRUE, the automatic modelling of the ARIMA model is enabled. If FALSE, the parameters of the ARIMA model can be specified.

Control variables for the automatic modelling of the ARIMA model (when automdl.enabled is set to TRUE):

automdl.acceptdefault

a logical. If TRUE, the default model (ARIMA(0,1,1)(0,1,1)) may be chosen in the first step of the automatic model identification. If the Ljung-Box Q statistics for the residuals is acceptable, the default model is accepted and no further attempt will be made to identify another model.

automdl.cancel

the cancellation limit (numeric). If the difference in moduli of an AR and an MA roots (when estimating ARIMA(1,0,1)(1,0,1) models in the second step of the automatic identification of the differencing orders) is smaller than the cancellation limit, the two roots are assumed equal and cancel out.

automdl.ub1

the first unit root limit (numeric). It is the threshold value for the initial unit root test in the automatic differencing procedure. When one of the roots in the estimation of the ARIMA(2,0,0)(1,0,0) plus mean model, performed in the first step of the automatic model identification procedure, is larger than the first unit root limit in modulus, it is set equal to unity.

automdl.ub2

the second unit root limit (numeric). When one of the roots in the estimation of the ARIMA(1,0,1)(1,0,1) plus mean model, which is performed in the second step of the automatic model identification procedure, is larger than second unit root limit in modulus, it is checked if there is a common factor in the corresponding AR and MA polynomials of the ARMA model that can be canceled (see automdl.cancel). If there is no cancellation, the AR root is set equal to unity (i.e. the differencing order changes).

automdl.mixed

a logical. This variable controls whether ARIMA models with non-seasonal AR and MA terms or seasonal AR and MA terms will be considered in the automatic model identification procedure. If FALSE, a model with AR and MA terms in both the seasonal and non-seasonal parts of the model can be acceptable, provided there are no AR or MA terms in either the seasonal or non-seasonal terms.

automdl.balanced

a logical. If TRUE, the automatic model identification procedure will have a preference for balanced models (i.e. models for which the order of the combined AR and differencing operator is equal to the order of the combined MA operator).

automdl.armalimit

the ARMA limit (numeric). It is the threshold value for t-statistics of ARMA coefficients and constant term used for the final test of model parsimony. If the highest order ARMA coefficient has a t-value smaller than this value in magnitude, the order of the model is reduced. If the constant term t-value is smaller than the ARMA limit in magnitude, it is removed from the set of regressors.

automdl.reducecv

numeric, ReduceCV. The percentage by which the outlier's critical value will be reduced when an identified model is found to have a Ljung-Box statistic with an unacceptable confidence coefficient. The parameter should be between 0 and 1, and will only be active when automatic outlier identification is enabled. The reduced critical value will be set to (1-ReduceCV)*CV, where CV is the original critical value.

automdl.ljungboxlimit

the Ljung Box limit (numeric). Acceptance criterion for the confidence intervals of the Ljung-Box Q statistic. If the LjungBox Q statistics for the residuals of a final model is greater than the Ljung Box limit, then the model is rejected, the outlier critical value is reduced and model and outlier identification (if specified) is redone with a reduced value.

automdl.ubfinal

numeric, final unit root limit. The threshold value for the final unit root test. If the magnitude of an AR root for the final model is smaller than the final unit root limit, then a unit root is assumed, the order of the AR polynomial is reduced by one and the appropriate order of the differencing (non-seasonal, seasonal) is increased. The parameter value should be greater than one.

Control variables for the non-automatic modelling of the ARIMA model (when automdl.enabled is set to FALSE):

arima.mu

logical. If TRUE, the mean is considered as part of the ARIMA model.

arima.p

numeric. The order of the non-seasonal autoregressive (AR) polynomial.

arima.d

numeric. The regular differencing order.

arima.q

numeric. The order of the non-seasonal moving average (MA) polynomial.

arima.bp

numeric. The order of the seasonal autoregressive (AR) polynomial.

arima.bd

numeric. The seasonal differencing order.

arima.bq

numeric. The order of the seasonal moving average (MA) polynomial.

Control variables for the user-defined ARMA coefficients. Coefficients can be defined for the regular and seasonal autoregressive (AR) polynomials and moving average (MA) polynomials. The model considers the coefficients only if the procedure for their estimation (arima.coefType) is provided, and the number of provided coefficients matches the sum of (regular and seasonal) AR and MA orders (p,q,bp,bq).

arima.coefEnabled

logical. If TRUE, the program uses the user-defined ARMA coefficients.

arima.coef

a vector providing the coefficients for the regular and seasonal AR and MA polynomials. The vector length must be equal to the sum of the regular and seasonal AR and MA orders. The coefficients shall be provided in the following order: regular AR (Phi; p elements), regular MA (Theta; q elements), seasonal AR (BPhi; bp elements) and seasonal MA (BTheta; bq elements). E.g.: arima.coef=c(0.6,0.7) with arima.p=1, arima.q=0,arima.bp=1 and arima.bq=0.

arima.coefType

a vector defining the ARMA coefficients estimation procedure. Possible procedures are: "Undefined" = no use of any user-defined input (i.e. coefficients are estimated), "Fixed" = the coefficients are fixed at the value provided by the user, "Initial" = the value defined by the user is used as the initial condition. For orders for which the coefficients shall not be defined, the arima.coef can be set to NA or 0, or the arima.coefType can be set to "Undefined". E.g.: arima.coef = c(-0.8,-0.6,NA), arima.coefType = c("Fixed","Fixed","Undefined").

fcst.horizon

the forecasting horizon (numeric). The forecast length generated by the RegARIMA model in periods (positive values) or years (negative values). By default, the program generates a two-year forecast (fcst.horizon set to -2).

x11.mode

character: the decomposition mode. Determines the mode of the seasonal adjustment decomposition to be performed: "Undefined" - no assumption concerning the relationship between the time series components is made; "Additive" - assumes an additive relationship; "Multiplicative" - assumes a multiplicative relationship; "LogAdditive" - performs an additive decomposition of the logarithms of the series being adjusted; "PseudoAdditive" - assumes an pseudo-additive relationship. Could be changed by the program, if needed.

x11.seasonalComp

logical: if TRUE, the program computes a seasonal component. Otherwise, the seasonal component is not estimated and its values are all set to 0 (additive decomposition) or 1 (multiplicative decomposition).

x11.lsigma

numeric: the lower sigma boundary for the detection of extreme values, > 0.5, default=1.5.

x11.usigma

numeric: the upper sigma boundary for the detection of extreme values, > lsigma, default=2.5.

x11.trendAuto

logical: automatic Henderson filter. If TRUE, an automatic selection of the Henderson filter's length for the trend estimation is enabled.

x11.trendma

numeric: the length of the Henderson filter. The user-defined length of the Henderson filter. The option is available when the automatic Henderson filter selection is disabled (x11.trendAuto=FALSE). Should be an odd number in the range (1, 101].

x11.seasonalma

a vector of character(s) specifying which seasonal moving average (i.e. seasonal filter) will be used to estimate the seasonal factors for the entire series. The vector can be of length: 1 - the same seasonal filter is used for all periods (e.g.: 'seasonal.filter = "Msr"' or 'seasonal.filter = "S3X3"' ); or have a different value for each quarter (length 4) or each month (length 12) - (e.g. for quarterly series: 'seasonal.filter = c("S3X3", "Msr", "S3X3", "Msr")'). Possible filters are: '"Msr"', '"Stable"', '"X11Default"', '"S3X1"', '"S3X3"', '"S3X5"', '"S3X9"', '"S3X15"'. '"Msr"' - the program chooses the final seasonal filter automatically.

x11.fcasts

numeric: the number of forecasts generated by the RegARIMA model in periods (positive values) or years (negative values).Default value: fcasts=-1.

x11.bcasts

numeric: the number of backcasts used in X11. Negative figures are translated in years of backcasts. Default value: bcasts=0.

x11.calendarSigma

character to specify if the standard errors used for extreme values detection and adjustment are computed: from 5 year spans of irregulars ("None", the default); separately for each calendar month/quarter ("All"); separately for each period only if Cochran’s hypothesis test determines that the irregular component is heteroskedastic by calendar month/quarter ("Signif"); separately for two complementary sets of calendar months/quarters specified by the x11.sigmaVector parameter ("Select", see parameter x11.sigmaVector).

x11.sigmaVector

a vector to specify one of the two groups of periods for whose standard errors used for extreme values detection and adjustment will be computed. Only used if x11.calendarSigma = "Select". Possible values are: "Group1" and "Group2".

x11.excludeFcasts

logical: to exclude forecasts and backcasts. If TRUE, the RegARIMA model forecasts and backcasts are not used during the detection of extreme values in the seasonal adjustment routines.

benchmarking.enabled

logical: to enable benchmarking. If TRUE, the benchmarking is enabled.

benchmarking.target

character: the target of the benchmarking procedure, which can be the raw series ("Original") or the series the adjusted for calendar effects ("CalendarAdjusted").

benchmarking.useforecast

logical: If TRUE, the forecasts of the seasonally adjusted variable and of the target variable are used in the benchmarking computation so the benchmarking constrains is also applied to the forecasting period.

benchmarking.rho

numeric: the value of the AR(1) parameter (set between 0 and 1) in the function used for benchmarking.

benchmarking.lambda

numeric: a parameter used for benchmarking that relatesto to the weights in the regression equation. It is typically equal to 0, 1/2 or 1.

Details

The available predefined 'JDemetra+' model specifications are described in the table below:

Identifier | Log/level detection | Outliers detection | Calendar effects | ARIMA
RSA0 | NA | NA | NA | Airline(+mean)
RSA1 | automatic | AO/LS/TC | NA | Airline(+mean)
RSA2c | automatic | AO/LS/TC | 2 td vars + Easter | Airline(+mean)
RSA3 | automatic | AO/LS/TC | NA | automatic
RSA4c | automatic | AO/LS/TC | 2 td vars + Easter | automatic
RSA5c | automatic | AO/LS/TC | 7 td vars + Easter | automatic
X11 | NA | NA | NA | NA

Value

A two-element list of class c("SA_spec", "X13"), containing: (1) an object of class c("regarima_spec", "X13") with the RegARIMA model specification; (2) an object of class c("X11_spec", "data.frame") with the X11 algorithm specification. Each component refers to different parts of the SA model specification, mirroring the arguments of the function (for details, see the function arguments in the description). Each lowest-level component (except span, pre-specified outliers, user-defined variables and pre-specified ARMA coefficients) is structured as a data frame with columns denoting different variables of the model specification and rows referring to:

  • first row: the base specification, as provided within the argument spec;

  • second row: user modifications as specified by the remaining arguments of the function (e.g.: arima.d);

  • and third row: the final model specification.

    The final specification (third row) shall include user modifications (row two) unless they were wrongly specified. The pre-specified outliers, user-defined variables and pre-specified ARMA coefficients consist of a list of Predefined (base model specification) and Final values.

  • regarima: an object of class c("regarima_spec", "x13"). See Value of the function regarima_spec_x13.

  • x11: a data.frame of class c("X11_spec", "data.frame"), containing the x11 variables in line with the names of the arguments variables. The final values can be also accessed with the function s_x11.

References

More information and examples related to 'JDemetra+' features in the online documentation: https://jdemetra-new-documentation.netlify.app/ BOX G.E.P. and JENKINS G.M. (1970), "Time Series Analysis: Forecasting and Control", Holden-Day, San Francisco.

BOX G.E.P., JENKINS G.M., REINSEL G.C. and LJUNG G.M. (2015), "Time Series Analysis: Forecasting and Control", John Wiley & Sons, Hoboken, N. J., 5th edition.

See Also

x13

Examples

myseries <- ipi_c_eu[, "FR"]
myspec1 <- x13_spec(spec = "RSA5c")
myreg1 <- x13(myseries, spec = myspec1)

# To modify a pre-specified model specification
myspec2 <- x13_spec(spec = "RSA5c", tradingdays.option = "WorkingDays")
myreg2 <- x13(myseries, spec = myspec2)

# To modify the model specification of a "X13" object
 myspec3 <- x13_spec(myreg1, tradingdays.option = "WorkingDays")
 myreg3 <- x13(myseries, myspec3)

# To modify the model specification of a "X13_spec" object
 myspec4 <- x13_spec(myspec1, tradingdays.option = "WorkingDays")
 myreg4 <- x13(myseries, myspec4)

# Pre-specified outliers
 myspec1 <- x13_spec(spec = "RSA5c", usrdef.outliersEnabled = TRUE,
             usrdef.outliersType = c("LS", "AO"),
             usrdef.outliersDate = c("2008-10-01", "2002-01-01"),
             usrdef.outliersCoef = c(36, 14),
             transform.function = "None")

 myreg1 <- x13(myseries, myspec1)
 myreg1
 s_preOut(myreg1)


# User-defined calendar regressors
 var1 <- ts(rnorm(length(myseries))*10, start = start(myseries), frequency = 12)
 var2 <- ts(rnorm(length(myseries))*100, start = start(myseries), frequency = 12)
 var <- ts.union(var1, var2)
 myspec1 <- x13_spec(spec = "RSA5c", tradingdays.option = "UserDefined",
                     usrdef.varEnabled = TRUE,
                     usrdef.var = var,
                     usrdef.varType = c("Calendar", "Calendar"))
 myreg1 <- x13(myseries, myspec1)
 myreg1

 myspec2 <- x13_spec(spec = "RSA5c", usrdef.varEnabled = TRUE,
             usrdef.var = var1, usrdef.varCoef = 2,
             transform.function = "None")
 myreg2 <- x13(myseries, myspec2)
 s_preVar(myreg2)

# Pre-specified ARMA coefficients
 myspec1 <- x13_spec(spec = "RSA5c", automdl.enabled = FALSE,
             arima.p = 1, arima.q = 1, arima.bp = 0, arima.bq = 1,
             arima.coefEnabled = TRUE,
             arima.coef = c(-0.8, -0.6, 0),
             arima.coefType = c(rep("Fixed", 2), "Undefined"))

 s_arimaCoef(myspec1)
 myreg1 <- x13(myseries, myspec1)
 myreg1

# To define a seasonal filter
 myspec1 <- x13_spec("RSA5c", x11.seasonalma = rep("S3X1", 12))
 mysa1 <- x13(myseries, myspec1)