AUTOMDL options ;

The AUTOMDL statement is used to invoke the automatic model selection procedure of the X-12-ARIMA method. This method is based largely on the TRAMO (time series regression with ARIMA noise, missing values, and outliers) method by Gomez and Maravall (1997a, 1997b). If the AUTOMDL statement is used without the OUTLIER statement, then only missing values regressors are included in the regARIMA model. If the AUTOMDL and the OUTLIER statements are used, then both missing values regressors and regressors for automatically identified outliers are included in the regARIMA model.

If both the AUTOMDL statement and the ARIMA statement are present, the ARIMA statement is ignored. The ARIMA statement specifies the model, while the AUTOMDL statement allows the X12 procedure to select the model. If the AUTOMDL statement is specified and a data set is specified in the MDLINFOIN= option of the PROC X12 statement, then the AUTOMDL statement is ignored if the specified data set contains a model specification for the series. If no model for the series is specified in the data set specified in the MDLINFOIN= option, then the AUTOMDL (or ARIMA) statement is used to determine the model. Thus, it is possible to give a specific model for some series and automatically identify the model for other series by using both the MDLINFOIN= option and the AUTOMDL statement.

When AUTOMDL is specified, the X12 procedure compares a model selected using a TRAMO method to a default model. The TRAMO method is implemented first, and involves two parts: identifying the orders of differencing and identifying the ARIMA model. The table "ARIMA Estimates for Unit Root Identification" provides details about the identification of the orders of differencing, while the table "Results of Unit Root Test for Identifying Orders of Differencing" shows the orders of differencing selected by TRAMO. The table "Models Estimated by Automatic ARIMA Model Selection Procedure" provides details regarding the TRAMO automatic model selection, and the table "Best Five ARIMA Models Chosen by Automatic Modeling" ranks the best five models estimated using the TRAMO method. The next available table, "Comparison of Automatically Selected Model and Default Model," compares the model selected by the TRAMO method to a default model. At this point in the processing, if the default model is selected over the TRAMO model, then PROC X12 displays a note. No note is displayed if the TRAMO model is selected. PROC X12 then performs checks for unit roots, over-differencing, and insignificant ARMA coefficients. If the model is changed due to any of these tests, a note is displayed. The last table, "Final Automatic Model Selection," shows the results of the automatic model selection.

The following options can appear in the AUTOMDL statement:

MAXORDER=(nonseasonal order, seasonal order)

specifies the maximum orders of nonseasonal and seasonal ARMA polynomials for the automatic ARIMA model identification procedure. The maximum order for the nonseasonal ARMA parameters should be between 1 and 4; the maximum order for the seasonal ARMA should be 1 or 2.

DIFFORDER=(nonseasonal order, seasonal order)

specifies the fixed orders of differencing to be used in the automatic ARIMA model identification procedure. When the DIFFORDER= option is used, only the AR and MA orders are automatically identified. Acceptable values for the regular differencing orders are 0, 1, and 2; acceptable values for the seasonal differencing orders are 0 and 1. If the MAXDIFF= option is also specified, then the DIFFORDER= option is ignored. There are no default values for DIFFORDER. If neither the DIFFORDER= option nor the MAXDIFF= option is specified, then the default is MAXDIFF=(2,1).

MAXDIFF=(nonseasonal order, seasonal order)

specifies the maximum orders of regular and seasonal differencing for the automatic identification of differencing orders. When MAXDIFF is specified, the differencing orders are identified first, and then the AR and MA orders are identified. Acceptable values for the regular differencing orders are 1 and 2; the only acceptable value for the seasonal differencing order is 1. If both the MAXDIFF= option and the DIFFORDER option= are specified, then the DIFFORDER= option is ignored. If neither the DIFFORDER= nor the MAXDIFF= option is specified, the default is MAXDIFF=(2,1).

NOINT

suppresses the fitting of a constant (or intercept) parameter in the model. (That is, the parameter is omitted.)

PRINT=UNITROOTTEST

PRINT=AUTOCHOICE

PRINT=UNITROOTTESTMDL

PRINT=AUTOCHOICEMDL

PRINT=BEST5MODEL

lists the tables to be displayed in the output.

PRINT=AUTOCHOICE displays the tables titled "Comparison of Automatically Selected Model and Default Model" and "Final Automatic Model Selection." The "Comparison of Automatically Selected Model and Default Model" table compares a default model to the model chosen by the TRAMO-based automatic modeling method. The "Final Automatic Model Selection" table indicates which model has been chosen automatically. If the PRINT= option is not specified, then PRINT=AUTOCHOICE is displayed by default.

PRINT=UNITROOTTEST causes the table titled "Results of Unit Root Test for Identifying Orders of Differencing" to be printed. This table displays the orders that were automatically selected by AUTOMDL. Unless the nonseasonal and seasonal differences are specified using the DIFFORDER= option, AUTOMDL automatically identifies the orders of differencing.

PRINT=UNITROOTMDL displays the table titled "ARIMA Estimates for Unit Root Identification." This table summarizes the various models that were considered by the TRAMO automatic selection method while identifying the orders of differencing and the statistics associated with those models. The unit root identification method first attempts to obtain the coefficients by using the Hannan-Rissanen method. If Hannan-Rissanen estimation cannot be performed, the algorithm attempts to obtain the coefficients by using conditional likelihood estimation.

PRINT=AUTOCHOICEMDL displays the table "Models Estimated by Automatic ARIMA Model Selection Procedure." This table summarizes the various models that were considered by the TRAMO automatic model selection method and their measures of fit.

PRINT=BEST5MODEL displays the table "Best Five ARIMA Models Chosen by Automatic Modeling." This table ranks the five best models that were considered by the TRAMO automatic modeling method.

BALANCED

specifies that the automatic modeling procedure prefer balanced models over unbalanced models. A balanced model is one in which the sum of AR, differencing, and seasonal differencing orders equal to the sum of MA and seasonal MA orders. Specifying BALANCED gives the same preference as the TRAMO program. If BALANCED is not specified, all models are given equal consideration.

HRINITIAL

specifies that Hannan-Rissanen estimation be done before exact maximum likelihood estimation to provide initial values. If HRINITIAL is specified, then models for which the Hannan-Rissanen estimation has an unacceptable coefficient are rejected.

ACCEPTDEFAULT

specifies that the default model be chosen if its Ljung-Box Q is acceptable.

LJUNGBOXLIMIT=value

specifies acceptance criteria for confidence coefficient of the Ljung-Box Q statistic. If the Ljung-Box Q for a final model is greater than this value, the model is rejected, the outlier critical value is reduced, and outlier identification is redone with the reduced value (see the REDUCECV option). The value specified must be greater than 0 and less than 1. The default value is 0.95.

REDUCECV=value

specifies the percentage that the outlier critical value be reduced when a final model is found to have an unacceptable confidence coefficient for the Ljung-Box Q statistic. This value should be between 0 and 1. The default value is 0.14286.

ARMACV=value

specifies the threshold value for the t statistics associated with the highest order ARMA coefficients. As a check of model parsimony, the parameter estimates and t statistics of the highest order ARMA coefficients are examined to determine if the coefficient is insignificant. An ARMA coefficient is considered to be insignificant if the absolute value of the parameter estimate is below 0.15 for 150 or fewer observations, and below 0.1 for more than 150 observations and the t value (displayed in the table "Exact ARMA Maximum Likelihood Estimation") is below the value specified in the ARMACV= option. If the highest order ARMA coefficient is found to be insignificant then the order of the ARMA model is reduced. For example, if AUTOMDL identifies a (3 1 1)(0 0 1) model and the parameter estimate of the seasonal MA lag of order 1 is –0.9 and its t value is –0.55, then the ARIMA model is reduced to at least (3 1 1)(0 0 0). After the model is reestimated, the check for insignificant coefficients is performed again. If ARMACV=0.54 is specified in the preceding example, then the coefficient is not found to be insignificant and the model is not reduced.

If a constant regressor is allowed in the model and if the t value (displayed in the table "Regression Model Parameter Estimates") is below the ARMACV= critical value, then the constant regressor is considered to be insignificant and is removed. Note that if a constant regressor is added to or removed from the model and then the ARIMA model changes, then the t statistic for the constant regressor also changes. Thus, changing the ARMACV= value does not necessarily add or remove a constant term from the model.

The value specified in the ARMACV= option should be greater than zero. The default value is 1.0.