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The State Space Model

In: Multivariate Time Series With Linear State Space Structure

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  • Víctor Gómez

    (Ministerio de Hacienda y Administraciones Públicas Dirección Gral. de Presupuestos, Subdirección Gral. de Análisis y P.E.)

Abstract

In this chapter, the state space model is thoroughly discussed. After defining the general state space model, the Kalman filter is derived. The square root covariance and the information filter are described. The topics of likelihood evaluation, forecasting, smoothing and covariance-based filters are discussed. Markov processes and the backwards Kalman filter are presented. The last part of the chapter is devoted to the handling of state space models with constant bias and incompletely specified initial conditions. The two-stage Kalman filter and the square root information form of the bias filter are described. Several algorithms for likelihood evaluation, forecasting and smoothing are given.

Suggested Citation

  • Víctor Gómez, 2016. "The State Space Model," Springer Books, in: Multivariate Time Series With Linear State Space Structure, chapter 0, pages 213-322, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-28599-3_4
    DOI: 10.1007/978-3-319-28599-3_4
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