I am trying to get more insight into how the confidence limits are calculated in PROC FORECAST using the METHOD=STEPAR option. The documentation doesn't appear to specify the calculation for the STEPAR option but it does for the other methods (e.g., EXPO, WINTERS, etc.)
"STEPAR uses the sigma value estimated from the historical data, but also some additional information beyond the end of the historical data when computing the confidence limits. The easiest way to think of the confidence limits produced by the STEPAR method is that the standard error is based on the sum of the standard error of the individual predicted value for the trend component and the standard error of the individual predicted value for the autoregressive error structure. A good description of the standard error of an individual predicted value may be found in the SAS/STAT User's Guide (SAS/STAT--> SAS/STAT User's Guide--> Introduction to Regression Procedures-->Statistical Background--> Predicted and Residual Values).
With other words: the confidence limits for the STEPAR method use the historical data for the estimate of sigma (root mean squared error). For a given future observation, it uses the known value of the time trend variable(s) for that future observation, and it uses the best linear predicted value(s) of the structural residuals for the autoregressive part of the model for that future observation."
Having shared this information please allow me to suggest not to use STEPAR for any serious forecasting task. You may want to have a look at more recent implementations of forecasting methods such as PROC ESM or PROC UCM (or SSM) depending on your needs.
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