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
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 |