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RegARIMA model specification: the pre-adjustment in X13

Source: R/regarima_specX13.R
regarima_spec_x13.Rd

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).

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.

Details

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

Identifier |Log/level detection |Outliers detection |Calendar effects |ARIMARG0 |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 |automaticRG4c |automatic |AO/LS/TC |
2 td vars + Easter |automaticRG5c |automatic |AO/LS/TC |7 td vars + Easter |automatic

References

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

Examples

# \donttest{
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
#> y = regression model + arima (2, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#>           Estimate Std. Error
#> Phi(1)     0.07859      0.114
#> Phi(2)     0.19792      0.076
#> Theta(1)  -0.48272      0.111
#> BTheta(1) -0.65916      0.043
#> 
#>               Estimate Std. Error
#> Monday         0.64094      0.228
#> Tuesday        0.81794      0.229
#> Wednesday      1.05374      0.229
#> Thursday       0.06981      0.228
#> Friday         0.93434      0.228
#> Saturday      -1.63686      0.226
#> Leap year      2.11550      0.697
#> Easter [1]    -2.38135      0.451
#> AO (9-2008)   31.95554      2.924
#> LS (9-2008)  -57.04093      2.657
#> TC (4-2020)  -35.62104      2.120
#> AO (3-2020)  -21.00931      2.145
#> AO (5-2011)   13.21877      1.832
#> TC (9-2008)   23.44654      4.001
#> TC (12-2001) -20.47521      2.922
#> AO (12-2001)  17.13461      2.962
#> TC (2-2002)   10.61731      1.937
#> 
#> Fixed outliers: 
#>              Coefficients
#> LS (10-2008)           36
#> AO (1-2002)            14
#> 
#> 
#> Residual standard error: 2.178 on 337 degrees of freedom
#> Log likelihood = -792.6, aic =  1629 aicc =  1632, bic(corrected for length) = 1.901
#> 
s_preOut(myreg1)
#>   type       date coeff
#> 1   LS 2008-10-01    36
#> 2   AO 2002-01-01    14


 # 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
#> y = regression model + arima (2, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#>           Estimate Std. Error
#> Phi(1)     0.01215      0.108
#> Phi(2)     0.16352      0.075
#> Theta(1)  -0.54810      0.102
#> BTheta(1) -0.66761      0.042
#> 
#>                Estimate Std. Error
#> r.var1       -1.257e-02      0.010
#> r.var2       -3.007e-04      0.001
#> Monday        5.585e-01      0.230
#> Tuesday       8.678e-01      0.230
#> Wednesday     1.039e+00      0.231
#> Thursday      4.572e-02      0.231
#> Friday        9.057e-01      0.232
#> Saturday     -1.546e+00      0.230
#> Leap year     2.134e+00      0.709
#> Easter [1]   -2.490e+00      0.467
#> TC (4-2020)  -3.541e+01      2.166
#> AO (3-2020)  -2.095e+01      2.182
#> AO (5-2011)   1.360e+01      1.870
#> LS (11-2008) -1.248e+01      1.631
#> 
#> 
#> Residual standard error: 2.212 on 340 degrees of freedom
#> Log likelihood = -798.2, aic =  1634 aicc =  1637, bic(corrected for length) = 1.883
#> 

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)
#> $series
#>               Jan          Feb          Mar          Apr          May
#> 1990 -15.34266387 -11.14761221  15.97811635  -6.39805078  15.66690553
#> 1991   2.25973337  -5.14857122  -8.23788240   3.34415250  -0.93490765
#> 1992  -1.29408799   4.07795520  -5.83968954  -1.93449890  -2.69546670
#> 1993   1.76436411  11.28307358   4.35001744   5.48833492   6.47418304
#> 1994 -11.87530126   3.62417465  -5.49435319   6.92949838  -0.60843916
#> 1995 -12.50367945  15.82132306  12.52529118  -2.09395701  -6.39033687
#> 1996   4.16082526 -12.95865368   6.82633090   4.96913333  14.39660656
#> 1997 -13.56043492  -3.14751072 -10.19265181  -6.12249656  -2.89068749
#> 1998  -7.33749597  -7.08484753  14.75092459   8.45004185  12.93994431
#> 1999   3.92236141   3.78419970   1.66175673  11.53387369   0.14748302
#> 2000   0.77160580   5.58395338  -1.66854367  -2.27980619   2.42666056
#> 2001 -17.98743117  -9.57051078  -4.74058606 -18.60461283   2.53690073
#> 2002  14.14224665   2.41625825 -14.36087478  -3.14552745  -4.80542811
#> 2003   5.99672514  -5.04358892  -4.06909625  -4.60935206  22.14908426
#> 2004  -7.63245040 -11.18492914  11.97977461   9.81193912  11.91749205
#> 2005  12.76706963   8.21075754   4.19785146  17.11661220 -22.15632715
#> 2006   6.13377167  14.83931321  -4.43773736   2.68589741 -12.28216829
#> 2007   0.59301839   8.48264703  25.75396587   0.94259964  -5.19949532
#> 2008   1.32582442  -9.74084022 -12.50949663  -0.46336042  11.37387771
#> 2009  -3.29112249   1.13049080  10.51229395   3.26977400   7.87037444
#> 2010   2.59523192  -7.73404126 -18.05527531   1.78383232  -5.25777309
#> 2011  -4.41476451  -2.46028129   3.65792190  -0.34132882   2.96227003
#> 2012   0.13030894   0.51249629   5.38638152   5.19672613 -24.22911275
#> 2013   0.01828103   1.40092252  -5.20598538  23.65811636 -16.96474415
#> 2014  14.56857971 -19.33784243  -8.80400798  -7.97730162  -8.86130974
#> 2015   1.73137014   5.77917253  -1.16008707   9.04521145  -0.16586710
#> 2016 -16.46117829  -1.23604069  -9.71640654  10.68587364  23.16252874
#> 2017 -19.41405982  14.15706719   5.96399657  -6.52922289  -1.54144673
#> 2018   3.62795564   7.70735944 -12.88986224  -7.13194370  -1.02383386
#> 2019  10.47205425 -15.46576348 -10.46005681 -22.72669757  -3.16651938
#> 2020  -2.14418765  16.74899343   1.16360148  14.26565587  -2.39667330
#>               Jun          Jul          Aug          Sep          Oct
#> 1990 -14.49155712  -7.91503959  -5.04480733   4.01826700   9.71396469
#> 1991   3.04062078  -4.76507534  -2.41311717   8.24155833 -15.55643970
#> 1992   0.73658232   3.57236138   5.50428418   0.38401793 -16.09575292
#> 1993   8.78463454   3.50797869   0.49879720   8.35749446  -2.81725199
#> 1994 -11.93540930  -1.19908059  -7.08107950 -16.16663973   4.95847824
#> 1995   3.98902937  13.41973500  -0.37607422   5.43670114  17.40218394
#> 1996  12.07358558   2.38514694  -2.98837878  13.84621050  -7.00069022
#> 1997  15.06983292   3.67722694  -0.20034941  -9.79921959 -14.00912333
#> 1998   2.98161142  -4.05682490  -1.38807578  -2.22592731  17.47150257
#> 1999   0.21440845  -8.26352170   0.47399133  -2.93107372  12.07632181
#> 2000  -9.28482969  15.15406678  -8.11598824  13.11247408   8.15566796
#> 2001  -2.14401713 -23.70181451   0.03258078   6.69745568   2.26820843
#> 2002   8.36254248  -0.52349287   9.51957625  14.94512798  -3.44214729
#> 2003  14.86967820  -3.55098858   8.76203737  -2.14696646  20.20798363
#> 2004   6.32833568   5.32825947  -8.20121900  -1.59325676  -0.17532122
#> 2005  -1.84878197   6.71168243  -7.95140242 -15.66257835  12.13732488
#> 2006   4.78528762  16.69859573  -0.36455545  -4.40936271   7.34408890
#> 2007   7.74428621  12.28289259  18.80606885  -1.25241723  -7.59094766
#> 2008  12.64449891  -5.48742076   6.82391430  -9.29773363  -9.75148693
#> 2009   4.41559619 -10.19304514  -1.58698326 -16.37701292  28.39266231
#> 2010   4.00186316  -1.22587586  -0.71345032  20.95734365  13.22082615
#> 2011  -2.21059772   1.87706159  -4.38062172  -0.88733579   6.34250029
#> 2012  -8.06290253  -4.84679992  -6.53077284  -2.93764247  -2.76989004
#> 2013   6.82585584  13.61561976  19.05955757  -6.72838542 -10.62911432
#> 2014  -2.94827785  -8.86651693   0.99084673   7.20546895  10.00469215
#> 2015  -9.22297409 -10.60114550 -17.87199640 -10.66551779 -11.29829171
#> 2016 -16.82873392   1.35875428   4.98437767  13.33462968  -0.22954568
#> 2017  -4.43645660  -5.18233778   2.06107064  16.39453666 -15.64734714
#> 2018  -6.47611750  -3.73253836   0.83347213   9.17216273  -2.58953302
#> 2019 -14.76190645  -1.00387827  -7.46222611   2.03645883   4.97450361
#> 2020 -11.05473915   3.22897729   0.21746800   3.17624820  -9.69700843
#>               Nov          Dec
#> 1990  -5.79663020  16.04179789
#> 1991   0.93501283  -3.66949421
#> 1992 -10.49710115  20.52033974
#> 1993  -7.91679461   0.01653727
#> 1994  12.99750970 -16.15985506
#> 1995  -3.24455939  -4.47511333
#> 1996  18.60931509  18.03924959
#> 1997  14.45014910  -4.23481621
#> 1998  -0.81704668   1.24141586
#> 1999   0.32001384   1.80397550
#> 2000   1.20032668   8.81789848
#> 2001  -5.91868492  -4.05414494
#> 2002   6.45775407 -15.34500551
#> 2003 -18.38661562   1.72937164
#> 2004  -3.90664205  -4.02775110
#> 2005  15.03810074 -11.69425021
#> 2006  -5.75309458   0.74897554
#> 2007  -5.09303603  -1.56039669
#> 2008  -0.27117079   4.46671886
#> 2009   9.61819160   5.08432001
#> 2010  12.00558995  -7.81874565
#> 2011   8.65538237  -4.30593090
#> 2012   1.36469589  10.67207722
#> 2013  16.33683158   5.40830359
#> 2014   5.27999513  11.63605931
#> 2015   3.87267796  12.70263382
#> 2016  -1.91523237  -4.40614893
#> 2017   5.11589918 -15.39661373
#> 2018   6.77025733  -4.20100735
#> 2019 -10.14286644  11.45760347
#> 2020  14.34467716  -9.88804847
#> 
#> $description
#>              type coeff
#> userdef Undefined     2
#> 

 # 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)
#>                Type Value
#> Phi(1)        Fixed  -0.8
#> Theta(1)      Fixed  -0.6
#> BTheta(1) Undefined   0.0
myreg1 <- regarima(myseries, myspec1)
myreg1
#> y = regression model + arima (1, 1, 1, 0, 1, 1)
#> Log-transformation: yes
#> Coefficients:
#>           Estimate Std. Error
#> Phi(1)     -0.8000       0.00
#> Theta(1)   -0.6000       0.00
#> BTheta(1)  -0.6977       0.04
#> 
#>              Estimate Std. Error
#> Monday       0.006317      0.002
#> Tuesday      0.007824      0.002
#> Wednesday    0.010528      0.002
#> Thursday     0.001857      0.002
#> Friday       0.010099      0.002
#> Saturday    -0.018439      0.002
#> Easter [1]  -0.020593      0.004
#> TC (4-2020) -0.475720      0.031
#> AO (3-2020) -0.213355      0.023
#> AO (5-2011)  0.143705      0.016
#> 
#> 
#> Residual standard error: 0.0256 on 347 degrees of freedom
#> Log likelihood = 802.3, aic =  1733 aicc =  1734, bic(corrected for length) = -7.15
#> 
# }