X13 Procedure

specifies that an AIC-based selection be used to determine whether a given set of regression variables are to be included with the specified regARIMA model. For example, if you specify a trading day model selection, then AIC values (with a correction for the length of the series, henceforth referred to as AICC) are derived for models with and without the specified trading day variable. By default, the model with a smaller AICC is used to generate forecasts, identify outliers, and so on. If you specify more than one type of regressor, the AIC tests are performed sequentially in this order: (a) trading day regressors, (b) Easter regressors, (c) user-defined regressors. If there are several variables of the same type (for example, several trading day regressors), then AIC-based selection is applied to them as a group. That is, either all variables of this type or none are included in the final model. If you do not specify this option, no automatic AIC-based selection is performed.

If you use the AUTOMDL statement to identify the model and you also specify this option, then this option affects the model selection process in the following manner:

For more information about the X-13ARIMA-SEATS automatic modeling method, see section 7.2 of the X-13ARIMA-SEATS Reference Manual, Version 1.1 (US Bureau of the Census 2013c).

specifies how the monthly means, which are used to remove seasonality from the EASTER predefined regressor, are calculated. When PREDEFINED=EASTER(w) is specified in the REGRESSION statement, monthly means are computed internally over the 500-year range from 1600 to 2099 by default. These monthly means are then used to remove seasonality from the Easter effect prior to calculating the Easter regression coefficient. The EASTERMEANS= option is ignored if no predefined EASTER regressor is included in the regression model or if SCEASTER(w) is the only predefined Easter regressor specified. You can specify the following values:

By default, EASTERMEANS=YR500.

specifies a list of the types of regression effects whose model-estimated values are not to be removed from the original series before performing the seasonal adjustment calculations that are specified by the X11 statement. The NOAPPLY= option applies to the regression component values displayed in the X11 seasonal adjustment method regARIMA component tables as shown in Table 4.

lists the predefined regression variables to be included in the model. Data values for these variables are calculated by the program, mostly as functions of the calendar. Table 5 gives definitions for the available predefined variables. The values LOM and LOQ are equivalent: the actual regression is controlled by the SEASONS= option in the PROC X13 statement. You can specify multiple predefined regression variables. The syntax for using both a length-of-month and a seasonal regression can be in one of the following forms:

regression predefined=lom seasonal;

regression predefined=(lom seasonal);

regression predefined=lom predefined=seasonal;

The following restrictions apply when you use more than one predefined regression variable:

The predefined regression variables, EASTER, LABOR, SCEASTER, SINCOS, TDSTOCK, and THANK, require extra parameters. Only one TDSTOCK regressor can be implemented in the regression model. If you specify multiple TDSTOCK variables, PROC X13 uses the last TDSTOCK variable specified. For EASTER, LABOR, SCEASTER, SINCOS, and THANK, you can specify the variables with different parameters to implement multiple regressors in the model. For example, the following statement specifies two EASTER regressors with widths 7 and 14:

regression predefined=easter(7) easter(14);

For SINCOS, specifying a parameter includes both the sine and the cosine regressor except for the highest order allowed (2 for quarterly data and 6 for monthly data.) For quarterly data, the following statement is the most common use of the SINCOS variable; it includes three regressors in the model:

regression predefined=sincos(1,2);

For monthly data, the following statement is the most common use of the SINCOS variable; it includes 11 regressors in the model:

regression predefined=sincos(1,2,3,4,5,6);

Table 5: Predefined Regression Variables in X-13ARIMA-SEATS

Regression Effect	Variable Definitions
Trend constant CONSTANT	where
	and
	is the number of the w days before Easter that fall in month
Easter holiday	(or quarter) t. (Note: This variable is 0 except in February, March,
EASTER(w)	and April (or first and second quarter).
	It is nonzero in February only for .)
	Restriction: .
Labor Day
LABOR(w)	(Note: This variable is 0 except in August and September.)
	Restriction: .
Length-of-month	where = length of month t (in days)
(monthly flow)	and (average length of month)
LOM
Stock length-of-month LOMSTOCK	where and are defined in LOM and
Length-of-quarter	where = length of quarter t (in days)
(quarterly flow)	and (average length of quarter)
LOQ
Leap year (monthly and quarterly flow) LPYEAR
Statistics Canada Easter	If Easter falls before April w, let be the number of the w days
(monthly or quarterly flow)	on or before Easter that fall in March. Then:
SCEASTER(w)
	If Easter falls on or after April w, then .
	(Note: This variable is 0 except in March and April (or first and
	second quarter).) Restriction: .
Fixed seasonal SEASONAL
Fixed seasonal
SINCOS(j)	, and s is the seasonal period
SINCOS()	for )
	Restrictions: , .
Trading day
TD, TDNOLPYEAR
One coefficient trading day
TD1COEF, TD1NOLPYEAR
Stock trading day TDSTOCK(w)
	where is the smaller of w and the length of month t.
	For end-of-month stock series, set w to 31; that is,
	specify TDSTOCK(31). Restriction: .
Thanksgiving	proportion of days from w days before Thanksgiving
THANK(w)	through December 24 that fall in month t (negative values of w indicate
	days after Thanksgiving).
	(Note: This variable is 0 except in November and December.)
	Restriction: .

specifies variables in the DATA= or AUXDATA= data set (which are specified in the PROC X13 statement) that are to be used as regressors. The variables in the data set should contain the values for each observation that define the regressor. Regression variables should also include future values in the data set for the forecast horizon if the time series is to be extended with regARIMA forecasts. Regression variables should include past values if the time series is to be extended with regARIMA backcasts. Missing values are not permitted within the data span, including backcasts and forecasts, of the user-defined regressors. Example 45.6 shows how to create an input data set that contains both the series to be seasonally adjusted and a user-defined input variable. Example 45.11 shows how to create an auxiliary data set that contains a user-defined input variable. For more information about specifying user-defined regression variables, see the section User-Defined Regression Variables.

All regression variables in the USERVAR= option apply to all time series to be seasonally adjusted unless the MDLINFOIN= data set specifies different regression information. You cannot specify the PREDEFINED= option and the USERVAR= option in the same REGRESSION statement; however, you can specify multiple REGRESSION statements.

specifies initial or fixed values for the regression parameters in the order in which they appear in a PREDEFINED= or USERVAR= option. Each B= list applies to the PREDEFINED= or USERVAR= variable list that immediately precedes the slash.

For example, the following statements set an initial value of 1 for the user-defined regressor, x:

regression predefined=LOM ;
regression uservar=x / b=1 2 ;

In this example, the B= option applies only to the USERVAR= option. The value 2 is discarded because there is only one variable in the USERVAR= list.

To assign an initial value of 1 to the LOM regressor and 2 to the x regressor, use the following statements:

regression predefined=LOM / b=1;
regression uservar=x / b=2 ;

An F immediately following the numerical value indicates that this is not an initial value, but a fixed value. For an example that uses fixed parameters, see Example 45.8. In PROC X13, individual parameters can be fixed while other parameters in the same model are estimated.

enables a variable that you define to be processed in the same manner as a US Census predefined variable. You can specify the following values: AO, CONSTANT, EASTER, HOLIDAY, LABOR, LOM, LOMSTOCK, LOQ, LPYEAR, LS, RP, SCEASTER, SEASONAL, TC, TD, TDSTOCK, THANKS, or USER. For example, the US Census Bureau EASTER(w) regression effects are included the "RegARIMA Holiday Component" table (A7). Specify USERTYPE=EASTER to define a variable that is processed exactly as the US Census predefined EASTER(w) variable, including inclusion in the A7 table. Each USERTYPE= list applies to the USERVAR= variable list that immediately precedes the slash. USERTYPE= does not apply to US Census predefined variables.

The same rules for assigning B= values to regression variables apply for USERTYPE= options. For example, the following statements specify that the user-defined regressor in the variable MyEaster be processed exactly as the US Census predefined LOM variable:

regression uservar=MyLOM;
regression uservar=MyEaster / usertype=LOM EASTER;

In this example, the USERTYPE= option applies only to the MyEaster variable in the second REGRESSION statement. The USERTYPE value EASTER is discarded because there is only one variable in the USERVAR= list.

To assign the USERTYPE value LOM to the MyLOM variable and EASTER to the MyEaster variable, use the following statements:

regression uservar=MyLOM / usertype=LOM;
regression uservar=MyEaster / usertype=EASTER;

The following USERTYPE= options specify that the regression effect be removed from the seasonally adjusted series: EASTER, HOLIDAY, LABOR, LOM, LOMSTOCK, LOQ, LPYEAR, SCEASTER, SEASONAL, TD, TDSTOCK, THANKS, and USER. When a regression effect is removed from the seasonally adjusted series, the level (mean) of the seasonally adjusted series can be altered. It is often desirable to use a zero-mean (mean-adjusted) regressor for effects that are to be removed from the seasonally adjusted series. For an example that specifies a zero-mean regressor, see Example 45.6.