The X12 Procedure

Example 37.4 RegARIMA Automatic Model Selection

This example demonstrates regARIMA modeling and TRAMO-based automatic model selection, which is available with the AUTOMDL statement. ODS SELECT statements are used to limit the displayed output to the model selection and estimation stages. The same data set is used as in the previous examples.

title 'TRAMO Automatic Model Identification';
ods select ModelEstimation.AutoModel.UnitRootTestModel
           ModelEstimation.AutoModel.UnitRootTest
           ModelEstimation.AutoModel.AutoChoiceModel
           ModelEstimation.AutoModel.Best5Model
           ModelEstimation.AutoModel.AutomaticModelChoice
           ModelEstimation.AutoModel.FinalModelChoice
           ModelEstimation.AutoModel.AutomdlNote;
proc x12 data=sales date=date;
   var sales;
   transform function=log;
   regression predefined=td;
   automdl maxorder=(1,1)
           print=unitroottest unitroottestmdl autochoicemdl best5model;
   estimate;
   x11;
   output out=out(obs=23) a1 a2 a6 b1 c17 c20 d1 d7 d8 d9 d10
                  d11 d12 d13 d16 d18;
run;

proc print data=out(obs=23);
   title 'Output Variables Related to Trading Day Regression';
run;

The automatic model selection output is shown in Output 37.4.1, Output 37.4.2, and Output 37.4.3. The first table, "ARIMA Estimate for Unit Root Identification," gives details of the method that TRAMO uses to automatically select the orders of differencing. The second table, "Results of Unit Root Test for Identifying Orders of Differencing," shows that a regular difference order of 1 and a seasonal difference order of 1 has been determined by TRAMO. The third table, "Models Estimated by Automatic ARIMA Model Selection Procedure," shows all the models examined by the TRAMO-based method. The fourth table, "Best Five ARIMA Models Chosen by Automatic Modeling," shows the top five models in order of rank and their BIC2 statistic. The fifth table, "Comparison of Automatically Selected Model and Default Model," compares the model selected by the TRAMO model to the default X-12-ARIMA model. The sixth table, "Final Automatic Model Selection," shows which model was actually selected.

Table 37.14 and Output 37.4.4 illustrate the regARIMA modeling method. Table 37.14 shows the relationship between the output variables in PROC X12 that results from a regARIMA model. Note that some of these formulas apply only to this example. Output 37.4.4 shows the values of these variables for the first 23 observations in the example.