The State Space Model

  • Víctor Gómez
Part of the Statistics and Computing book series (SCO)


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 {Yt} is a multivariate process with \(Y_{t}\in \mathbb {R}^{p}\), Wt, Tt, Ht, Xt, Zt, and Gt 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 {𝜖t} is a sequence of uncorrelated stochastic vectors, \(\epsilon _{t}\in \mathbb {R}^{s}\), with zero mean and common covariance matrix σ2I.


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Authors and Affiliations

  • Víctor Gómez
    • 1
  1. 1.General Directorate of BudgetsMinistry of Finance and Public AdministrationsMadridSpain

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