SSM Procedure

Predefined Trend Models

The statistical models that govern the predefined trend components available in the SSM procedure are divided into two groups: models that are applicable to equally spaced data (possibly with replication), and models that are applicable more generally (the irregular data type). Each trend component can be described as a dot product bold upper Z alpha alpha Subscript t for some (time-invariant) vector bold upper Z and a state vector alpha alpha Subscript t. The component specification is complete after the vector bold upper Z is specified and the system matrices that govern the equations of alpha alpha Subscript t are specified. For trend models for regular data, all the system matrices are time-invariant. For irregular data, bold upper T Subscript t and bold upper Q Subscript t depend on the spacing between the distinct time points: left-parenthesis tau Subscript t plus 1 Baseline minus tau Subscript t Baseline right-parenthesis.

Last updated: June 19, 2025