The State Space Model

Abstract

The state space model considered in SSMMATLAB is

$$\displaystyle \begin {array}{rcl} \alpha _{t+1} &=& W_t\beta + T_t\alpha _t + H_t\epsilon _t, \\ Y_t &=& X_t\beta + Z_t\alpha _t + G_t\epsilon _t, \qquad t=1,\ldots ,n, \end {array}$$

where {Y _t} is a multivariate process with $Y_{t}\in \mathbb {R}^{p}$, W _t, T _t, H _t, X _t, Z _t, and G _t are time-varying deterministic matrices, $\beta \in \mathbb {R}^{q}$ is a constant bias vector, $\alpha _{t}\in \mathbb {R}^{r}$ is the state vector, and {𝜖 _t} is a sequence of uncorrelated stochastic vectors, $\epsilon _{t}\in \mathbb {R}^{s}$, with zero mean and common covariance matrix σ ²I.