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) );
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