The X12 Procedure

Example 38.2 Model Estimation

After studying the output from Example 38.1 and identifying the ARIMA part of the model as, for example, (0 1 1)(0 1 1) 12, you can replace the IDENTIFY statement with the ARIMA and ESTIMATE statements as follows:

proc x12 data=sales date=date;
   var sales;
   transform power=0;
   arima model=( (0,1,1)(0,1,1) );
   estimate;
run ;

The parameter estimates and estimation summary statistics are shown in Output 38.2.1.

Output 38.2.1: Estimation Data

The X12 Procedure

Exact ARMA Likelihood Estimation Iteration Tolerances
For Variable sales
Maximum Total ARMA Iterations	1500
Convergence Tolerance	1.0E-05

Average absolute percentage error in within-sample forecasts:
For Variable sales
Last year:	2.81
Last-1 year:	6.38
Last-2 year:	7.69
Last three years:	5.63

Exact ARMA Likelihood Estimation Iteration Summary
For Variable sales
Number of ARMA iterations	6
Number of Function Evaluations	19

Exact ARMA Maximum Likelihood Estimation
For Variable sales
Parameter	Lag	Estimate	Standard Error	t Value	Pr > \|t\|
Nonseasonal MA	1	0.40181	0.07887	5.09	<.0001
Seasonal MA	12	0.55695	0.07626	7.30	<.0001

Estimation Summary
For Variable sales
Number of Observations	144
Number of Residuals	131
Number of Parameters Estimated	3
Variance Estimate	1.3E-03
Standard Error Estimate	3.7E-02
Standard Error of Variance	1.7E-04
Log likelihood	244.6965
Transformation Adjustment	-735.2943
Adjusted Log likelihood	-490.5978
AIC	987.1956
AICC (F-corrected-AIC)	987.3845
Hannan Quinn	990.7005
BIC	995.8211