X13 Procedure

Example 45.2 Model Estimation

(View the complete code for this example.)

After studying the output from Example 45.1 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 x13 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 45.2.1.

Output 45.2.1: Estimation Data

The X13 Procedure

Exact ARMA Likelihood Estimation Iteration Tolerances
For Variable sales
Maximum Total ARMA Iterations1500
Convergence Tolerance1.0E-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 iterations6
Number of Function Evaluations19

Exact ARMA Maximum Likelihood Estimation
For Variable sales
ParameterLagEstimateStandard
Error
t ValuePr > |t|
Nonseasonal MA10.401810.078875.09<.0001
Seasonal MA120.556950.076267.30<.0001

Estimation Summary
For Variable sales
Number of Observations144
Number of Residuals131
Number of Parameters Estimated3
Variance Estimate1.3E-03
Standard Error Estimate3.7E-02
Standard Error of Variance1.7E-04
Log likelihood244.6965
Transformation Adjustment-735.2943
Adjusted Log likelihood-490.5978
AIC987.1956
AICC (F-corrected-AIC)987.3845
Hannan Quinn990.7005
BIC995.8211


Last updated: June 19, 2025