The X13 Procedure

AUTOMDL Statement

AUTOMDL options;

The AUTOMDL statement invokes the automatic model selection procedure of the X-13ARIMA-SEATS method. This method is based largely on the TRAMO (time series regression with ARIMA noise, missing values, and outliers) method by Gómez 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 both 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. For more information about missing value regressors, see the section Missing Values.

If both the AUTOMDL statement and the ARIMA statement are present, the ARIMA statement is ignored. The ARIMA statement specifies the model, but the AUTOMDL statement allows the X13 procedure to select the model. If the AUTOMDL statement is specified and a data set is specified in the MDLINFOIN= option in the PROC X13 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 MDLINFOIN= data set, 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 the AUTOMDL statement is specified, the X13 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, and 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 "Comparison of Automatically Selected Model and Default Model" table 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 X13 displays a note. No note is displayed if the TRAMO model is selected. The Ljung-Box Q statistic is then checked for acceptance, and the results are displayed in the "Check of the Residual Ljung-Box Q Statistic" table. The initial model selected at this point is displayed in the "Initial Automatic Model Selection" table. PROC X13 then performs final checks for unit roots, overdifferencing, and insignificant ARMA coefficients. The results of the final checks are displayed in the "Final Checks for Identified Model" table, which also indicates changes to the model order if the orders are changed. The last table, "Final Automatic Model Selection," shows the results of the automatic model selection; if the orders have been altered during the final checks, the Orders Altered column displays a value of Yes. An example of the automatic modeling selection procedure is shown in Example 45.4.

The following options can appear in the AUTOMDL statement:

ACCEPTDEFAULT

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

ARMACV=value

specifies the threshold value for the t statistics that are 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 whether the coefficient is insignificant. An ARMA coefficient is considered to be insignificant if the t value that is displayed in the table "Exact ARMA Maximum Likelihood Estimation" is below the value specified in the ARMACV= option and the absolute value of the parameter estimate is reliably close to zero. The absolute value is considered to be reliably close to zero if it is below 0.15 for 150 or fewer observations or is below 0.1 for more than 150 observations. 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 –0.09 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 is allowed in the model and if the t value associated with the constant parameter estimate is below the ARMACV= critical value, then the constant is considered to be insignificant and is removed from the model. Note that if a constant is added to or removed from the model and then the ARIMA model changes, then the t statistic for the constant parameter estimate 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.

BALANCED

specifies that the automatic modeling procedure prefer balanced models over unbalanced models. A balanced model is one in which the sum of the AR, seasonal AR, differencing, and seasonal differencing orders equals the sum of the 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.

DIFFID=CONDITIONAL | EXACT | EXACTFIRST

specifies the estimation to be used in automatic difference identification when Hannen-Rissanen fails. You can specify the following values:

CONDITIONAL: uses conditional likelihood estimation.
EXACT: uses exact likelihood estimation.
EXACTFIRST: attempts to estimate the parameters by using exact likelihood for the first diffiditer iterations, where diffiditer is specified in the DIFFIDITER= option. If the estimation does not converge within diffiditer iterations, then conditional likelihood is used to estimate the parameters.

The effects of this option are displayed in the Estimation Method column in the "ARIMA Estimates for Unit Root Identification" table. By default, DIFFID=EXACTFIRST.

DIFFIDITER=diffiditer

specifies the maximum number of exact likelihood estimation iterations when DIFFID=EXACTFIRST is specified. If the number of iterations exceeds diffiditer, then conditional likelihood is used to estimate the remaining iterations. The default value is 500; this default differs from the default value of 200 in the US Census Bureau’s implementation of X-13ARIMA-SEATS.

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 (nonseasonal) 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).

HRINITIAL

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

LJUNGBOXLIMIT=value

specifies acceptance criteria for the 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 for more information. The value specified in the LJUNGBOXLIMIT= option must be greater than 0 and less than 1. The default value is 0.95.

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).

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 is 4, and the maximum order for the seasonal ARMA is 2.

NOINT

suppresses the fitting of a constant or intercept parameter in the model.

PRINT=(option-list)

specifies the tables to be displayed in the output. You can specify one or more of the following options (parentheses are optional; use a space between options):

NONE: suppresses all automatic modeling output.
ALL: includes all automatic modeling tables in the output if NONE is not specified in the option-list.
ONLY: specifies that only the listed tables be output.
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. These tables are output by default unless NONE or ONLY is specified in the option-list.
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.
AUTOLJUNGBOX: displays the table "Check of the Residual Ljung-Box Q Statistic." This table is displayed only if the model is not accepted because the Ljung-Box Q statistic is greater than the acceptance limit. The details of the test and the changes made either to the model or to the model selection method are displayed.
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.
FINALCHECKS: displays the table "Final Checks for Identified Model." This table displays the results of the final checks for model adequacy. The final checks can result in the orders of the initially identified model being altered. Any order changes or changes in the constant term are included in this table. This table is output by default unless NONE or ONLY is specified in the option-list.
INITCHOICEMDL: displays the table "Initial 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 chosen model can then be altered if the model fails the Ljung-Box Q statistic test. The "Initial Automatic Model Selection" table indicates which model has been chosen automatically after the Ljung-Box Q statistic test. This table is output by default unless NONE or ONLY is specified in the option-list.
UNITROOTTEST: displays the table titled "Results of Unit Root Test for Identifying Orders of Differencing." This table displays the orders that were automatically selected by the AUTOMDL statement. Unless the nonseasonal and seasonal differences are specified using the DIFFORDER= option, the AUTOMDL statement automatically identifies the orders of differencing. This table is output by default unless NONE or ONLY is specified in the option-list.
UNITROOTTESTMDL: 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 it identified 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.

By default, PRINT=(UNITROOTTEST AUTOCHOICE INITCHOICEMDL FINALCHECKS).

REDUCECV=value

specifies the percentage by which 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.