FORECAST Statement

The X12 Procedure

FORECAST Statement

FORECAST options;

The FORECAST statement is used to forecast the time series using the estimated model. The output contains point forecast and forecast statistics for the transformed and original series.

The following option can appear in the FORECAST statement.

LEAD= value

Specifies the number of periods ahead to forecast. The default is the number of periods in a year (4 or 12) and the maximum is 60.

Forecasts and Standard Errors Tables are displayed in association with the FORECAST statement. Confidence limits are also included. If the data are transformed, then two tables will be displayed, one table for the original data, and one table for the transformed data.

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. Table A6 provides information related to trading-day effects. Table A8 provides information related to outlier factors. 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= CONSTANT

PREDEFINED= LOM

PREDEFINED= LOMSTOCK

PREDEFINED= LOQ

PREDEFINED= LPYEAR

PREDEFINED= SEASONAL

PREDEFINED= TD

PREDEFINED= TDNOLPYEAR

PREDEFINED= TD1COEF

PREDEFINED= TD1NOLPYEAR

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 can be used. The syntax for using both a length-of-month and a seasonal regression could be in one of the following forms:

   regression predefined=lom seasonal;

   regression predefined=(lom seasonal);

   regression predefined=lom predefined=seasonal;

Certain restrictions apply when using more than one predefined regression variable. Only one of TD, TDNOLPYEAR, TD1COEF, or TD1NOLPYEAR may be specified. LPYEAR cannot be used with TD, TD1COEF, LOM, LOMSTOCK, or LOQ. LOM or LOQ cannot be used with TD or TD1COEF.

Table 6.1: Predefined Regression Variables in X-12-ARIMA

Regression Effect

Variable Definitions

Trend Constant

$(1- B)^{-d}(1- B^s)^{-D}I(t \geq 1),$

CONSTANT

where $I(t \geq 1)=\cases{1 & for t \geq 1\cr 0 & for t \lt 1\space \cr}$

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

Stock Length-of-Month

LOMSTOCK

$SLOM_t=\cases{m_t - \bar{m} - \mu(l) & for t=1\cr SLOM_{t-1} + m_t - \bar{m} & otherwise\cr}$

where $\bar{m}$ and m_t are defined in LOM and

$\mu(l)=\cases{0.375 & when 1st February in series is a leap year\cr 0.125 & w... ...eries is a leap year\cr -0.375 & when 4th February in series is a leap year\cr}$

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

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

Fixed Seasonal

SEASONAL

$M_{1,t}=\cases{1 & in January\cr -1 & in December\cr 0 & otherwise\cr}$ ,..., $M_{11,t}=\cases{1 & in November\cr -1 & in December\cr 0 & otherwise\cr}$

Trading Day

T_1,t = (no. of Mondays) - (no. of Sundays), ...,

TD, TDNOLPYEAR

T_6,t =(no. of Saturdays) - (no. of Sundays)

One Coefficient Trading Day

(no. of weekdays) - (5/2)(no. of Saturdays and Sundays)

TD1COEF, TD1NOLPYEAR

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