This section discusses the computation of predicted values and confidence limits for external forecast models.

Given a response time series and external forecast series , the prediction errors are computed as for those t for which both and are nonmissing. The mean squared error (MSE) is computed from the prediction errors.

The variance of the k-step-ahead prediction errors is set to k times the MSE. From these variances, the standard errors and confidence limits are computed in the usual way. If the supplied predictions contain so many missing values within the time range of the response series that the MSE estimate cannot be computed, the confidence limits, standard errors, and statistics of fit are set to missing.