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The X12 Procedure

Example 34.8 Setting Regression Parameters

This example illustrates the use of fixed regression parameters in PROC X12. Suppose that you have the same data set as in the section Basic Seasonal Adjustment. You can specify the following statements to use TRAMO to automatically identify a model that includes a U.S. Census Bureau Easter(25) regressor:

title 'Estimate Easter(25) Parameter';
proc x12 data=sales date=date MdlInfoOut=mdlout1;
   var sales;
   regression predefined=easter(25);
   automdl;
run ;

The displayed results are shown in Output 34.8.1.

Output 34.8.1 Automatic Model ID with Easter(25) Regression

Estimate Easter(25) Parameter

The X12 Procedure

Regression Model Parameter Estimates
For Variable sales
Type	Parameter	NoEst	Estimate	Standard Error	t Value	Pr > |t|
Easter	Easter[25]	Est	-5.09298	3.50786	-1.45	0.1489

Exact ARMA Maximum Likelihood Estimation
For Variable sales
Parameter	Lag	Estimate	Standard Error	t Value	Pr > |t|
Nonseasonal AR	1	0.62148	0.09279	6.70	<.0001
	2	0.23354	0.10385	2.25	0.0262
	3	-0.07191	0.09055	-0.79	0.4285
Nonseasonal MA	1	0.97377	0.03771	25.82	<.0001
Seasonal MA	12	0.10558	0.10205	1.03	0.3028

The MDLINFOOUT= data set, mdlout1, that contains the model and parameter estimates is shown in Output 34.8.2.

proc print data=mdlout1;
run;

To fix the Easter(25) parameter while adding a regressor that is weighted according to the number of Saturdays in a month, either use the REGRESSION and EVENT statements or create a MDLINFOIN= data set. The following statements show the method for using the REGRESSION statement to fix the EASTER parameter and the EVENT statement to add the SATURDAY regressor. The output is shown in Output 34.8.3.

title 'Use SAS Statements to Alter Model';
proc x12 data=sales date=date MdlInfoOut=mdlout2grm;
   var sales;
   regression predefined=easter(25) / b=-5.029298 F;
   event Saturday;
   automdl;
run ;

To fix the EASTER regressor and add the new SATURDAY regressor by using a DATA step, you can create the data set mdlin2 as shown. The data set mdlin2 is displayed in Output 34.8.4.

title 'Use a SAS DATA Step to Create a MdlInfoIn= Data Set';
data plusSaturday;
   _NAME_ = 'sales';
   _MODELTYPE_ = 'REG';
   _MODELPART_ = 'EVENT';
   _COMPONENT_ = 'SCALE';
   _PARMTYPE_ = 'USER';
   _DSVAR_ = 'SATURDAY';
run;

data mdlin2;
   set mdlout1;
   if ( _DSVAR_ = 'EASTER' ) then do;
       _NOEST_ = 1;
       _EST_ = -5.029298;
       end;
run;

proc append base=mdlin2 data=plusSaturday force;
run;

proc print data=mdlin2;
run;

The data set mdlin2 can be used to replace the regression and model information contained in the REGRSSION, EVENT, and AUTOMDL statements. Note that the model specified in the mdlin2 data set is the same model as the automatically identified model. The following example uses the mdlin2 data set as input; the results are displayed in Output 34.8.5.

title 'Use Updated Data Set to Alter Model';
proc x12 data=sales date=date MdlInfoIn=mdlin2 MdlInfoOut=mdlout2DS;
   var sales;
   estimate;
run ;

The following statements specify almost the same information as contained in the data set mdlin2. Note that the ARIMA statement is used to specify the lags of the model. However, the initial AR and MA parameter values are the default. When using the mdlin2 data set as input, the initial values can be specified. The results are displayed in Output 34.8.6.

title 'Use SAS Statements to Alter Model';
proc x12 data=sales date=date MdlInfoOut=mdlout3grm;
   var sales;
   regression predefined=easter(25) / b=-5.029298 F;
   event Saturday;
   arima model=((3 1 1)(0 1 1));
   estimate;
run ;

proc print data=mdlout3grm;
run;

The MDLINFOOUT= data set provides a method for comparing the results of the model identification. The data set mdlout3grm that is the result of using the ARIMA MODEL= option can be compared to the data set mdlout2DS that is the result of using the MDLINFOIN= data set with initial values for the AR and MA parameters. The mdlout2DS data set is shown in Output 34.8.7, and the results of the comparison are shown in Output 34.8.8. The slight difference in the estimated parameters can be attributed to the difference in the initial values for the AR and MA parameters.

proc print data=mdlout2DS;
run;

title 'Compare Results of SAS Statement Input and MdlInfoIn= Input';
proc compare base= mdlout3grm compare=mdlout2DS;
var _EST_;
run ;

                                                                                
                                                                                
                     Value Comparison Results for Variables                     
                                                                                
           __________________________________________________________           
                      ||  Value of Parameter Estimate                           
                      ||       Base    Compare                                  
                  Obs ||      _EST_      _EST_      Diff.     % Diff            
            ________  ||  _________  _________  _________  _________            
                      ||                                                        
                   1  ||     3.4176     3.4176  0.0000225   0.000658            
                   5  ||     0.6223     0.6222  -0.000033  -0.005237            
                   6  ||     0.3043     0.3043  -0.000021  -0.006977            
                   7  ||    -0.1486    -0.1486  0.0000235    -0.0158            
                   8  ||     0.9713     0.9713  -0.000024  -0.002452            
                   9  ||     0.1168     0.1169  0.0000759     0.0650            
           __________________________________________________________           

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