The 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 $\mb{Z} \pmb {\alpha }_{t}$ for some (time-invariant) vector $\mb{Z}$ and a state vector $ \pmb {\alpha }_{t}$. The component specification is complete after the vector $\mb{Z}$ is specified and the system matrices that govern the equations of $ \pmb {\alpha }_{t}$ are specified. For trend models for regular data, all the system matrices are time-invariant. For irregular data, $\mb{T}_{t}$ and $\mb{Q}_{t}$ depend on the spacing between the distinct time points: $(\tau _{t+1} - \tau _{t})$.