The ESM Procedure

The multistep forecasts generated by the preceding steps can optionally be summed from the STARTSUM= value to the LEAD= value. For example, if the options STARTSUM=4 and LEAD=6 are specified on the PROC ESM statement, the four-step through six-step ahead forecasts are summed.

The forecasts are simply summed; however, the prediction error variance of this sum is computed by taking into account the correlation between the individual predictions. (These variance-related computations are performed only when no transformation is specified; that is, when TRANSFORM=NONE.) The upper and lower confidence limits for the sum of the predictions is then computed based on the prediction error variance of the sum.

The forecast summation is particularly useful when it is desirable to model in one frequency but the forecast of interest is another frequency. For example, if a time series has a monthly frequency (INTERVAL=MONTH) and you want a forecast for the third and fourth future months, a forecast summation for the third and fourth month can be obtained by specifying STARTSUM=3 and LEAD=4.