REGRESSION Statement

The X12 Procedure

REGRESSION Statement

REGRESSION options ;

The REGRESSION statement includes regression variables in a regARIMA model or specifies regression variables whose effects are to be removed by the IDENTIFY statement to aid in ARIMA model identification. Predefined regression variables are selected with the PREDEFINED option. The only currently available predefined variables are length-of-month, length-of-quarter, and leap year. Table A6 provides information related to trading-day effects. You should note that missing values in the input series automatically create missing value regressors. Combining your model with additional predefined regression variables may result in a singularity problem. If a singularity occurs, then you may need to alter either the model or the choices of the predefined regressors in order to successfully perform the regression.

The following options can appear in the REGRESSION statement.

PREDEFINED= LOM

PREDEFINED= LOQ

PREDEFINED= LPYEAR

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. The values LOM and LOQ are actually equivalent: the actual regression is controlled by the PROC X12 SEASONS= option. Multiple predefined regression variables may be used. The syntax for using both a length-of-month and a leap-year regression could be one of the following forms:

   regression predefined=lom lpyear;

   regression predefined=(lom lpyear);

   regression predefined=lom predefined=lpyear;

Table 5.1: Predefined Regression Variables in X-12-ARIMA

Regression Effect

Variable Definitions

Length-of-Month

$m_t - \bar{m}$ where m_t = length of month t (in days)

(monthly flow)

and $\bar{m}=30.4375$ (average length of month)

LOM

Length-of-Quarter

$q_t - \bar{q}$ where q_t = length of quarter t (in days)

(quarterly flow)

and $\bar{q}=91.3125$ (average length of quarter)

LOQ

Leap Year

(monthly and quarterly flow)

LPYEAR

$LY_t=\cases{0.75 & in leap year February (first quarter)\cr -0.25 & in other Februaries (first quarter)\cr 0 & otherwise\cr}$

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