Implementation of states space models

The state vector can often be split in independent blocks; each block has its own initialization and dynamics. The transition matrices $T_t$, the covariances of the transition innovations $V_t$ and the initialization matrices are then block diagonal.

Univariate models are defined by a single equation, which reassemble the various block by means of different loading factors. Multi-variate models are straightforward extensions; they only differ by the number of equations.

The framework provides numerous building blocks – elements of the state vector or loading factors – that can be combined to create the actual state space model. Some blocks are self-sufficient - they represent an actual model - but in most cases, the user will need to glue several of them.

We present in this documentation the different matrices of each block. See the general model for the meaning of each matrix