The X13 Procedure

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 UnitRootTestModel
           UnitRootTest
           AutoChoiceModel
           Best5Model
           AutomaticModelChoice
           InitialModelChoice
           FinalModelChecks
           FinalModelChoice
           AutomdlNote;
proc x13 data=sales date=date;
   var sales;
   transform function=log;
   regression predefined=td;
   automdl maxorder=(1,1)
           print=all;
   estimate;
   x11;
   output out=out a1 a2 a6 b1 c17 c20 d1 d7 d8 d9 d10
                  d11 d12 d13 d16 d18;
run;

proc print data=out(obs=21);
   title 'Output Variables Related to Trading Day Regression';
run;

The automatic model selection output is shown in Output 45.4.1, Output 45.4.2, and Output 45.4.3. The first table, "ARIMA Estimate for Unit Root Identification" in Output 45.4.1, 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" in Output 45.4.1, 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" in Output 45.4.2, shows all the models examined by the TRAMO-based method. The fourth table, "Best Five ARIMA Models Chosen by Automatic Modeling" in Output 45.4.3, shows the top five models in order of rank and their BIC2 statistic. The fifth table, "Comparison of Automatically Selected Model and Default Model" in Output 45.4.3, compares the model selected by the TRAMO model to the default regARIMA model of the X-13ARIMA-SEATS method. The sixth table, "Initial Automatic Model Selection" in Output 45.4.3, shows which model was selected between the two models that are compared in the table "Comparison of Automatically Selected Model and Default Model." (When available, the table "Check of the Residual Ljung-Box Q Statistic" in Output 45.4.3 contains additional information about the initial model choice.) The seventh table, "Final Checks for Identified Model" in Output 45.4.3, displays the results of the final model checks for model adequacy. The eighth table, "Final Automatic Model Selection" in Output 45.4.3, shows which model was actually selected.

Table 45.16 and Output 45.4.4 illustrate the regARIMA modeling method. Table 45.16 shows the relationship between the output variables in PROC X13 that results from a regARIMA model. Note that some of these formulas apply only to this example. Output 45.4.4 shows the values of these variables for the first 21 observations in the example.