Example 37.2 Model Estimation

After studying the output from Example 37.1 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 37.2.1.

Output 37.2.1 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