model specification X13. It can be a character of 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".

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

The time span of the series to be used for the estimation of the RegARIMA model coefficients (default from 1900-01-01 to 2020-12-31) 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 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.

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

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

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

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

numeric specifying the number of periods excluded at the beginning of the series. Can be combined with estimate.exclLast.

numeric specifying the number of periods excluded at the end of the series. Can be combined with estimate.exclFirst.

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.

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.

pre-adjustment of the input series for 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".

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 if they are enabled (usrdef.outliersEnabled=TRUE) and the outliers' type (usrdef.outliersType) and date (usrdef.outliersDate) are provided.

logicals. If TRUE the program uses the pre-specified outliers.

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").

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").

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

Control variables for the user-defined variables:

logicals. If TRUE the program uses the user-defined variables.

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

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

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

defines the type of 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 have to be defined by the usrdef.var argument with usrdef.varType set to "Calendar" and usrdef.varEnabled = TRUE). "None" has also to be chosen for the "day-of-week effects" correction (tradingdays.stocktd to be modified accordingly).

logicals. 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".

option for including 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 was not pre-adjusted (transform.adjust set to "None") and the automatic correction for the leap-year effect was not selected (tradingdays.autoadjust set to FALSE).

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".

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.

logicals. If TRUE the program considers the Easter effect in the model.

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

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

defines the pre-tests for the significance of the Easter effect based on the t-statistic (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 belong 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.

logicals. 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 (default from 1900-01-01 to 2020-12-31) 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 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.

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

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

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

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

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

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

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

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

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

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

logicals. 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 inputted critical value (outlier.cv).

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

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

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

logicals. 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):

logicals. 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 any other.

numeric, cancelation 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 cancelation limit, the two roots are assumed equal and cancel out.

numeric, 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.

numeric, 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 cancelled (see automdl.cancel). If there is no cancellation, the AR root is set equal to unity (i.e. the differencing order changes).

logicals. The 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 not AR and MA terms in either the seasonal or non-seasonal.

logicals. 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).

numeric, arma limit. 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 less than this value in magnitude, the order of the model is reduced. Also if the constant term has a t-value less than arma limit in magnitude, it is removed from the set of regressors.

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)xCV, where CV is the original critical value.

numeric, Ljung Box limit. 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, the model is rejected, the outlier critical value is reduced, and model and outlier identification (if specified) is redone with a reduced value.

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 less than the final unit root limit, 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 (automdl.enabled is set to FALSE):

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

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

numeric. Regular differencing order.

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

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

numeric. Seasonal differencing order.

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).

logicals. If TRUE the program uses the user-defined ARMA coefficients.

vector providing the coefficients for the regular and seasonal AR and MA polynominals. The length of the vector must equal the sum of the regular and seasonal AR and MA orders. The coefficients shall be provided in the 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.

vector defining 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").

numeric, forecasts horizon. 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).

character, 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.

logicals. 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).

numeric, lower sigma boundary for the detection of extreme values.

numeric, upper sigma boundary for the detection of extreme values.

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

numeric, 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].

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 - same seasonal filters for all periods (e.g.: seasonalma=c("Msr")); or period's number - a seasonal filer is defined for each period (e.g. for quarterly series: seasonalma=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.

numeric, RegARIMA forecast. Length of the forecasts generated by the RegARIMA model in periods (positive values) or years (negative values).

numeric, backcast. Length of the backcasts used in X11. Negative figures are translated in years of backcasts.

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).

vector to specifies 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". Possibe values are: "Group1" and "Group2".

logicals, exclude forecats and backcasts. If TRUE forecasts and backcasts from the RegARIMA model are not used in the generation of extreme values in the seasonal adjustment routines.

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

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.