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 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 |
Last updated: June 19, 2025