Linear Time Series with MATLAB and OCTAVE pp 281-304 | Cite as

# The State Space Model

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## Abstract

The state space model considered in SSMMATLAB is where {

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

*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*^{2}*I*.## References

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