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Erschienen in:
2019 | OriginalPaper | Buchkapitel
10. The State Space Model
verfasst von : Víctor Gómez
Erschienen in: Linear Time Series with MATLAB and OCTAVE
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Abstract
The state space model considered in SSMMATLAB is 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.
$$\displaystyle \begin {array}{rcl} \alpha _{t+1} &=& W_t\beta + T_t\alpha _t + H_t\epsilon _t, \\ Y_t &=& X_t\beta + Z_t\alpha _t + G_t\epsilon _t, \qquad t=1,\ldots ,n, \end {array}$$