X13 Procedure

(View the complete code for this example.)

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 17 and Output 45.4.4 illustrate the regARIMA modeling method. Table 17 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.

Table 17: regARIMA Output Variables and Descriptions

Table	Title	Type	Formula
A1	Time series data (for the span analyzed)	Data	Input
A2	Prior-adjustment factors leap year (from trading day regression) adjustments	Factor	Calculated from regression
A6	RegARIMA trading day component leap year prior adjustments included from Table A2	Factor	Calculated from regression
B1	Original series (prior adjusted)	Data	*
	(adjusted for regARIMA factors)		*Because only TD specified
C17	Final weights for irregular component	Factor	Calculated using moving standard deviation
C20	Final extreme value adjustment factors	Factor	Calculated using C16 and C17
D1	Modified original data, D iteration	Data	**
			** in this example
D7	Preliminary trend cycle, D iteration	Data	Calculated using Henderson
			moving average
D8	Final unmodified SI ratios	Factor	***
			***TD specified in regression
D9	Final replacement values for SI ratios	Factor	If C17 shows extreme values,
			;
			otherwise
D10	Final seasonal factors	Factor	Calculated using moving averages
D11	Final seasonally adjusted data	Data	****
	(also adjusted for trading day)
			**** for this example
D12	Final trend cycle	Data	Calculated using Henderson moving average
D13	Final irregular component	Factor
D16	Combined adjustment factors (includes seasonal, trading day factors)	Factor
D18	Combined calendar adjustment factors	Factor
	(includes trading day factors)		*****
			*****Regression TD is the only calendar adjustment factor in this example