The 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 ($\hat{y}_{t, i} $), residuals ($\nu _{t,i}$), and their standard errors ($\sqrt { F_{t, i}}$). In addition, one-step-ahead forecasts of the components that are specified in the MODEL statements, and any other user-defined linear combinations of $\pmb {\alpha }_{t}$, are also produced. These forecasts are set to missing as long as the index $t < t_{*}$ (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 $\hat{y}_{t, i} $ and $\nu _{t,i}$) are reported as missing. When the fitted model is appropriate, the one-step-ahead residuals $\nu _{t,i}$ form a sequence of uncorrelated normal variates. This fact can be used during model diagnostic process.