X-13ARIMA model specification, SA/X13

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
)

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.

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.

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

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

# \donttest{
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
#> RegARIMA
#> 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
#> 
#> 
#> 
#> Decomposition
#> Monitoring and Quality Assessment Statistics:
#>       M stats
#> M(1)    0.151
#> M(2)    0.097
#> M(3)    1.206
#> M(4)    0.558
#> M(5)    1.041
#> M(6)    0.037
#> M(7)    0.082
#> M(8)    0.242
#> M(9)    0.062
#> M(10)   0.267
#> M(11)   0.252
#> Q       0.366
#> Q-M2    0.399
#> 
#> Final filters: 
#> Seasonal filter:  3x5
#> Trend filter:  13 terms Henderson moving average
#> 
#> 
#> Final
#> Last observed values
#>              y        sa        t            s           i
#> Jan 2020 101.0 102.89447 102.9447  -1.89446776  -0.0502488
#> Feb 2020 100.1 103.56224 102.9860  -3.46224124   0.5762734
#> Mar 2020  91.8  82.81896 103.2071   8.98103618 -20.3881828
#> Apr 2020  66.7  66.62390 103.6164   0.07610348 -36.9925073
#> May 2020  73.7  78.88976 104.0255  -5.18976181 -25.1357871
#> Jun 2020  98.2  87.30845 104.3450  10.89154932 -17.0365408
#> Jul 2020  97.4  92.39390 104.4861   5.00609785 -12.0921816
#> Aug 2020  71.7  97.51560 104.3380 -25.81559971  -6.8224392
#> Sep 2020 104.7  97.40102 103.9044   7.29897634  -6.5033820
#> Oct 2020 106.7  98.39408 103.3109   8.30592464  -4.9168409
#> Nov 2020 101.6 100.23574 102.7824   1.36426365  -2.5467131
#> Dec 2020  96.6  99.67219 102.4984  -3.07218537  -2.8261840
#> 
#> Forecasts:
#>                y_f     sa_f      t_f          s_f         i_f
#> Jan 2021  94.41766 101.0272 102.4220  -6.60952495 -1.39481900
#> Feb 2021  97.82331 101.6172 102.4196  -3.79385040 -0.80247216
#> Mar 2021 114.01485 102.1273 102.3712  11.88751670 -0.24388469
#> Apr 2021 102.04691 102.0672 102.2273  -0.02033583 -0.16002624
#> May 2021  95.95071 101.4262 102.0682  -5.47547024 -0.64200227
#> Jun 2021 112.61492 101.2166 101.9501  11.39833187 -0.73348910
#> Jul 2021 104.00289 101.5502 101.9316   2.45263829 -0.38137799
#> Aug 2021  79.03331 102.3155 102.0544 -23.28216183  0.26109558
#> Sep 2021 108.98851 102.3414 102.2480   6.64711680  0.09343944
#> Oct 2021 108.49736 102.1909 102.4372   6.30644391 -0.24626669
#> Nov 2021 106.32534 102.4451 102.6074   3.88025741 -0.16229864
#> Dec 2021  99.71313 102.9154 102.7518  -3.20223190  0.16356694
#> 
#> 
#> Diagnostics
#> Relative contribution of the components to the stationary
#> portion of the variance in the original series,
#> after the removal of the long term trend
#>  Trend computed by Hodrick-Prescott filter (cycle length = 8.0 years)
#>            Component
#>  Cycle         1.625
#>  Seasonal     41.918
#>  Irregular     0.727
#>  TD & Hol.     1.851
#>  Others       55.678
#>  Total       101.800
#> 
#> Combined test in the entire series
#>  Non parametric tests for stable seasonality
#>                                                           P.value
#>    Kruskall-Wallis test                                      0.000
#>    Test for the presence of seasonality assuming stability   0.000
#>    Evolutive seasonality test                                0.042
#>  
#>  Identifiable seasonality present
#> 
#> Residual seasonality tests
#>                                       P.value
#>  qs test on sa                          0.974
#>  qs test on i                           0.779
#>  f-test on sa (seasonal dummies)        0.921
#>  f-test on i (seasonal dummies)         0.826
#>  Residual seasonality (entire series)   0.770
#>  Residual seasonality (last 3 years)    0.894
#>  f-test on sa (td)                      0.974
#>  f-test on i (td)                       0.988
#> 
#> 
#> Additional output variables
 s_preOut(myreg1)
#>   type       date coeff
#> 1   LS 2008-10-01    36
#> 2   AO 2002-01-01    14


# 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"))
#> Warning: With tradingdays.option = "UserDefined", the parameters tradingdays.autoadjust, tradingdays.leapyear and tradingdays.stocktd are ignored.
 myreg1 <- x13(myseries, myspec1)
 myreg1
#> RegARIMA
#> y = regression model + arima (3, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#>           Estimate Std. Error
#> Phi(1)      0.3595      0.209
#> Phi(2)      0.1177      0.210
#> Phi(3)     -0.3259      0.155
#> Theta(1)   -0.6771      0.192
#> BTheta(1)  -0.7343      0.039
#> 
#>              Estimate Std. Error
#> Easter [8]     -2.891      0.686
#> TC (4-2020)   -36.231      2.021
#> AO (3-2020)   -22.969      2.463
#> LS (11-2008)  -12.368      1.610
#> AO (5-2011)     9.825      2.265
#> TC (2-2009)    -8.128      1.857
#> 
#> 
#> Residual standard error: 2.839 on 347 degrees of freedom
#> Log likelihood = -889.4, aic =  1803 aicc =  1804, bic(corrected for length) = 2.267
#> 
#> 
#> 
#> Decomposition
#> Monitoring and Quality Assessment Statistics:
#>       M stats
#> M(1)    0.376
#> M(2)    0.310
#> M(3)    3.000
#> M(4)    0.733
#> M(5)    2.377
#> M(6)    0.514
#> M(7)    0.116
#> M(8)    0.294
#> M(9)    0.074
#> M(10)   0.369
#> M(11)   0.334
#> Q       0.818
#> Q-M2    0.881
#> 
#> Final filters: 
#> Seasonal filter:  3x5
#> Trend filter:  23-Henderson
#> 
#> 
#> Final
#> Last observed values
#>              y        sa        t          s             i
#> Jan 2020 101.0 103.76443 103.7718  -2.764432  -0.007371637
#> Feb 2020 100.1 104.34515 103.9252  -4.245147   0.419965250
#> Mar 2020  91.8  81.04300 104.1168  10.757002 -23.073821166
#> Apr 2020  66.7  68.07471 104.2936  -1.374714 -36.218923904
#> May 2020  73.7  77.34542 104.4050  -3.645424 -27.059534745
#> Jun 2020  98.2  88.68292 104.4313   9.517080 -15.748342655
#> Jul 2020  97.4  93.46921 104.3778   3.930791 -10.908580688
#> Aug 2020  71.7  95.43752 104.2570 -23.737519  -8.819459329
#> Sep 2020 104.7  99.17267 104.0850   5.527329  -4.912314376
#> Oct 2020 106.7  97.12864 103.8669   9.571357  -6.738282414
#> Nov 2020 101.6  99.69487 103.6276   1.905134  -3.932784061
#> Dec 2020  96.6 102.36060 103.4003  -5.760595  -1.039736263
#> 
#> Forecasts:
#>                y_f     sa_f      t_f         s_f         i_f
#> Jan 2021  98.44952 101.2056 103.1901  -2.7560785 -1.98454698
#> Feb 2021  98.43821 102.5471 103.0165  -4.1088538 -0.46944312
#> Mar 2021 110.75460 101.9734 102.8973   8.7811716 -0.92383422
#> Apr 2021 103.71542 102.9016 102.8411   0.8138272  0.06051994
#> May 2021  99.53055 103.1863 102.8510  -3.6557369  0.33528360
#> Jun 2021 111.31381 101.6749 102.8754   9.6388933 -1.20051449
#> Jul 2021 105.69802 101.5389 102.9077   4.1591091 -1.36882965
#> Aug 2021  79.42133 103.3872 102.9666 -23.9658420  0.42058783
#> Sep 2021 108.59095 102.9687 103.0586   5.6222373 -0.08983556
#> Oct 2021 112.00799 102.4761 103.1532   9.5318659 -0.67704911
#> Nov 2021 105.36088 103.8747 103.2467   1.4862299  0.62793860
#> Dec 2021  98.66941 104.3502 103.4522  -5.6808324  0.89800432
#> 
#> 
#> Diagnostics
#> Relative contribution of the components to the stationary
#> portion of the variance in the original series,
#> after the removal of the long term trend
#>  Trend computed by Hodrick-Prescott filter (cycle length = 8.0 years)
#>            Component
#>  Cycle         1.963
#>  Seasonal     59.842
#>  Irregular     3.416
#>  TD & Hol.     0.172
#>  Others       34.046
#>  Total        99.439
#> 
#> Combined test in the entire series
#>  Non parametric tests for stable seasonality
#>                                                           P.value
#>    Kruskall-Wallis test                                      0.000
#>    Test for the presence of seasonality assuming stability   0.000
#>    Evolutive seasonality test                                0.269
#>  
#>  Identifiable seasonality present
#> 
#> Residual seasonality tests
#>                                       P.value
#>  qs test on sa                          0.000
#>  qs test on i                           0.002
#>  f-test on sa (seasonal dummies)        0.813
#>  f-test on i (seasonal dummies)         0.754
#>  Residual seasonality (entire series)   0.568
#>  Residual seasonality (last 3 years)    1.000
#>  f-test on sa (td)                      0.000
#>  f-test on i (td)                       0.000
#> 
#> 
#> Additional output variables

 myspec2 <- x13_spec(spec = "RSA5c", usrdef.varEnabled = TRUE,
             usrdef.var = var1, usrdef.varCoef = 2,
             transform.function = "None")
 myreg2 <- x13(myseries, myspec2)
 s_preVar(myreg2)
#> $series
#>               Jan          Feb          Mar          Apr          May
#> 1990  -4.93380941 -12.28615839  12.84563150  12.11780172   0.17867075
#> 1991  17.91430812  -8.01034578  -5.57933180   7.56117489  -0.65654280
#> 1992   6.99530402  -4.78932287 -13.14202741  -9.03645819  -6.82677769
#> 1993   6.85714751 -15.74190181 -10.39202637  10.62892692 -12.79380891
#> 1994   6.55348285   2.08748369   4.79304525  11.19721889   3.58970059
#> 1995 -16.27036866  10.95973351 -11.30615770   7.49407597   5.07040903
#> 1996 -16.41368825   1.85576753   8.08139505   4.62741902  -1.40862948
#> 1997  21.10958544   1.06319181   2.88638282  -8.28129022   2.59246188
#> 1998   7.49492399  13.68161796   8.09041925  10.52043916  15.76710173
#> 1999  14.61477127  -3.93734253   5.88577012 -10.59461309   7.02083603
#> 2000  -4.70589637  26.18843475  17.81970431   3.11227898   6.04652922
#> 2001   6.97447152   8.50194263  -2.82469962  10.56820511  -1.64563751
#> 2002   6.45915651   2.86538618 -19.55302496  -0.70122520 -19.93476957
#> 2003  -4.71600217  -3.86758443  -0.32921492 -15.89925204 -16.31630380
#> 2004 -15.66243530  -8.27262343  10.43432242  -5.61818713   4.58990225
#> 2005 -13.44497531  -0.07853537  -7.09360740  14.19910316  21.00753869
#> 2006  16.38748991   7.14250476   0.21730272  -7.10864161   0.67650247
#> 2007  19.42670865   4.54756408  -4.35878269  16.42250741  -1.19391302
#> 2008  -6.44304935  -3.17781887 -26.11142582  -4.04070180  19.63939389
#> 2009  -4.30394846  13.18921431   7.86662563   3.90908196   5.55016634
#> 2010  -3.55226178   9.79276002 -11.74070697  -3.96460863   0.28959344
#> 2011   3.71975670   7.52496103  -8.44102704 -14.74703765  -1.27286512
#> 2012   3.04153582  -1.56110528   6.66411599 -21.43024893  -7.85684050
#> 2013  15.28664770   2.85760869   9.66478863   0.41676859  -1.86568045
#> 2014   9.16852243  11.82521119   0.89920960 -14.23925932   1.85840157
#> 2015  18.72999491  -9.15749659  -0.12128002 -11.17237976   2.69965596
#> 2016 -15.34357208   0.26618737   3.62927093  -6.77324332  -3.86793166
#> 2017  -1.52302024  13.18666001  -7.75961869  11.48134828  11.40960766
#> 2018 -11.51931160  -8.74614335  -0.56005464  -6.48120780   2.67518834
#> 2019   1.30699486   8.77061311   5.57893934  11.50015537  -2.82304681
#> 2020  -1.61878192   5.52162660   3.48733451  -0.62679216  -4.82827570
#>               Jun          Jul          Aug          Sep          Oct
#> 1990  17.00247776  13.44115353   2.47249503  -0.95850995  -1.05894771
#> 1991  14.03825101   8.06123109  -1.25334438  -5.64422544   9.40777992
#> 1992   3.74599658   8.09784422 -10.27311894   2.71204716   3.72163386
#> 1993 -17.65259960 -23.94684943   6.61851420   2.79202139 -19.75798133
#> 1994  11.98583489   5.63019465   3.60364311   8.25363990  -0.40392584
#> 1995   1.49227768   7.56914894  -4.27224530 -13.47831121   0.82595585
#> 1996 -18.30167300   4.04087877  -0.13750674  -1.02241238   2.02454445
#> 1997  -4.95230738  -2.89501667   6.40683953  -1.41462861  -8.79847386
#> 1998  11.52029911  -5.17742857  -6.35012824  -4.00123911   5.93241461
#> 1999  -2.54390092  -3.80451079   7.22051799  13.27842786  -1.25492499
#> 2000   8.02925361  -7.42182079 -10.86486271  15.85888347  -1.40704169
#> 2001  -5.05197318  -4.02419900  22.95251358  -0.58040167   1.22377660
#> 2002   1.21132684   4.35595856   1.38904324   9.82497501  -2.86391397
#> 2003  -6.19216932  -4.28563857  21.43623439  13.81055332  -9.81823126
#> 2004   4.61175487   5.88209678  13.65187644   2.37584966 -13.01932383
#> 2005   0.56429659   8.05545122  -1.92729984  -1.20578134  -2.41185306
#> 2006  18.67312976   7.39326267   9.65687441   4.69334931   7.32928056
#> 2007   0.03403357  -2.87662480  10.04914840 -15.19681487  10.80588866
#> 2008  -9.08038236   2.31002822  10.83031391 -10.23062790  19.75884923
#> 2009   4.95861493 -15.88836847  -3.21264477 -15.52052891   9.61515998
#> 2010 -14.70506429   9.65172228  -7.81441694  12.57319338 -20.46247314
#> 2011  -1.13083340  18.06296611  -9.16313634   3.26036046  17.29406356
#> 2012   8.56316142  -3.54721322   1.86108946   3.85897720   6.05504903
#> 2013 -13.51099737  -9.53225887 -12.82607152  13.48738780   0.87489524
#> 2014   6.47343621   1.23381550  -5.57040623  -4.24403791  14.21456362
#> 2015  15.11653990  -5.93155678 -16.14954366 -13.73896551  11.92737540
#> 2016  -2.10774079  -6.33652476   0.79569318   2.38637053  -5.11546412
#> 2017  -3.34901191   6.29659134   7.34016764  18.02049619 -11.48480057
#> 2018   3.49756194 -12.17302032   0.81927914  -7.95643416  -5.84737942
#> 2019 -17.42631121   4.01343311   6.49059795  10.87865196  11.59117507
#> 2020  19.95979803 -12.51509572   5.28487960 -12.47616265  -0.41651340
#>               Nov          Dec
#> 1990 -12.61154714 -17.60210399
#> 1991  12.69808946  12.65038490
#> 1992 -14.73803514 -14.22799149
#> 1993   4.96506933  13.53031635
#> 1994  -6.05456736  -4.78648838
#> 1995  11.53728116  25.86841900
#> 1996   8.03320548  -5.87793245
#> 1997  -5.23639611  -6.13436596
#> 1998  -0.01094905 -18.90227763
#> 1999  11.39794704  -7.84406639
#> 2000  -9.75276634  -0.91846724
#> 2001  -2.00777681   4.60803569
#> 2002  16.94152064   5.21310799
#> 2003  13.12917276   3.72374042
#> 2004  17.37977175  14.64151538
#> 2005  -2.55729561  -2.08778684
#> 2006  13.33797734  13.30182641
#> 2007   4.35371426 -13.89147408
#> 2008   5.01748489   9.33783648
#> 2009 -10.86315269 -17.16257245
#> 2010  18.19078188 -13.67382107
#> 2011   6.18631030  -2.43510381
#> 2012   5.22120605  16.07831850
#> 2013  -5.66758222   5.73972934
#> 2014  -8.10897493  -6.78534611
#> 2015   1.16453951   1.97141988
#> 2016  -8.20642372 -14.97546434
#> 2017  12.16381354  -6.73465522
#> 2018   5.34806561  -5.30695812
#> 2019 -15.10504494   1.14206605
#> 2020 -10.54737293  -0.98173680
#> 
#> $description
#>              type coeff
#> userdef Undefined     2
#> 

# 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)
#>                Type Value
#> Phi(1)        Fixed  -0.8
#> Theta(1)      Fixed  -0.6
#> BTheta(1) Undefined   0.0
 myreg1 <- x13(myseries, myspec1)
 myreg1
#> RegARIMA
#> 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
#> 
#> 
#> 
#> Decomposition
#> Monitoring and Quality Assessment Statistics:
#>       M stats
#> M(1)    0.097
#> M(2)    0.052
#> M(3)    0.750
#> M(4)    0.749
#> M(5)    0.731
#> M(6)    0.126
#> M(7)    0.075
#> M(8)    0.220
#> M(9)    0.075
#> M(10)   0.293
#> M(11)   0.281
#> Q       0.300
#> Q-M2    0.331
#> 
#> Final filters: 
#> Seasonal filter:  3x5
#> Trend filter:  13 terms Henderson moving average
#> 
#> 
#> Final
#> Last observed values
#>              y        sa        t         s         i
#> Jan 2020 101.0 103.50059 103.4716 0.9758398 1.0002804
#> Feb 2020 100.1 103.70789 104.1959 0.9652110 0.9953168
#> Mar 2020  91.8  85.02419 105.2353 1.0796927 0.8079439
#> Apr 2020  66.7  66.06576 106.3700 1.0096002 0.6210940
#> May 2020  73.7  77.29646 107.2332 0.9534719 0.7208256
#> Jun 2020  98.2  88.21419 107.6348 1.1131996 0.8195693
#> Jul 2020  97.4  92.04371 107.5406 1.0581929 0.8558971
#> Aug 2020  71.7  95.53300 106.9592 0.7505260 0.8931720
#> Sep 2020 104.7  97.32774 105.9849 1.0757467 0.9183169
#> Oct 2020 106.7  98.74148 104.7928 1.0805996 0.9422542
#> Nov 2020 101.6 100.23569 103.5604 1.0136110 0.9678964
#> Dec 2020  96.6  99.45166 102.3889 0.9713262 0.9713127
#> 
#> Forecasts:
#>                y_f     sa_f       t_f       s_f       i_f
#> Jan 2021  91.86627 99.03608 101.33234 0.9276040 0.9773393
#> Feb 2021  93.73814 98.76312 100.39814 0.9491209 0.9837146
#> Mar 2021 109.97904 99.04192  99.55589 1.1104292 0.9948373
#> Apr 2021  99.51314 98.51411  98.84092 1.0101410 0.9966935
#> May 2021  92.44138 97.26558  98.27297 0.9504018 0.9897491
#> Jun 2021 109.51917 97.80126  97.82297 1.1198135 0.9997780
#> Jul 2021  99.72232 96.85484  97.49522 1.0296059 0.9934317
#> Aug 2021  74.93973 97.28720  97.30419 0.7702938 0.9998254
#> Sep 2021 104.15955 97.30940  97.21500 1.0703955 1.0009711
#> Oct 2021 102.57254 96.84676  97.16553 1.0591221 0.9967193
#> Nov 2021 100.68100 96.97009  97.14932 1.0382686 0.9981552
#> Dec 2021  94.63045 97.42206  97.13060 0.9713452 1.0030007
#> 
#> 
#> Diagnostics
#> Relative contribution of the components to the stationary
#> portion of the variance in the original series,
#> after the removal of the long term trend
#>  Trend computed by Hodrick-Prescott filter (cycle length = 8.0 years)
#>            Component
#>  Cycle         5.183
#>  Seasonal     82.105
#>  Irregular     1.148
#>  TD & Hol.     3.365
#>  Others       10.592
#>  Total       102.393
#> 
#> Combined test in the entire series
#>  Non parametric tests for stable seasonality
#>                                                           P.value
#>    Kruskall-Wallis test                                      0.000
#>    Test for the presence of seasonality assuming stability   0.000
#>    Evolutive seasonality test                                0.406
#>  
#>  Identifiable seasonality present
#> 
#> Residual seasonality tests
#>                                       P.value
#>  qs test on sa                          1.000
#>  qs test on i                           0.939
#>  f-test on sa (seasonal dummies)        0.990
#>  f-test on i (seasonal dummies)         0.972
#>  Residual seasonality (entire series)   0.989
#>  Residual seasonality (last 3 years)    0.996
#>  f-test on sa (td)                      0.994
#>  f-test on i (td)                       0.959
#> 
#> 
#> Additional output variables

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