SSM Procedure

Forecasting Phase

After the model-fitting phase, the filtering process is repeated again to produce the model-based one-step-ahead response variable forecasts (ModifyingAbove y With caret Subscript t comma i), residuals (nu Subscript t comma i), and their standard errors (StartRoot upper F Subscript t comma i Baseline EndRoot). In addition, one-step-ahead forecasts of the components that are specified in the MODEL statements, and any other user-defined linear combinations of alpha alpha Subscript t, are also produced. These forecasts are set to missing as long as the index t less-than t Subscript asterisk (that is, until the filtering process is initialized). If the filtering process remains uninitialized, then all the quantities that are related to the one-step-ahead forecast (such as ModifyingAbove y With caret Subscript t comma i and nu Subscript t comma i) are reported as missing. When the fitted model is appropriate, the one-step-ahead residuals nu Subscript t comma i form a sequence of uncorrelated normal variates. This fact can be used during model diagnostic process.

Last updated: June 19, 2025