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State-Space Models and the Kalman Filter

In: Time Series Econometrics

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  • Klaus Neusser

    (University of Bern)

Abstract

The state space representation is a flexible technique originally developed in automatic control engineering to represent, model, and control dynamic systems. Thereby the unobserved or partially observed state of a system in period t is summarized by an m-dimensional vector X t $$X_t$$ . The evolution of the state is then described by a VAR model of order one usually called the state equation. A second equation describes the connection between the state and the observations given by a n-dimensional vector Y t $$Y_t$$ . Despite its simple structure, state space models encompass a large variety of model classes: VARMA, respectively, VARIMA models (VARIMA models stand for vector autoregressive integrated moving-average models); unobserved-component models; factor models; structural time series models that decompose a given time series into a trend, a seasonal, and a cyclical component; models with measurement errors; VAR models with time-varying parameters, etc. See the examples given in Sect. 17.2.

Suggested Citation

  • Klaus Neusser, 2025. "State-Space Models and the Kalman Filter," Springer Texts in Business and Economics, in: Time Series Econometrics, edition 0, chapter 17, pages 335-362, Springer.
    • Handle: RePEc:spr:sptchp:978-3-031-88838-0_17
    DOI: 10.1007/978-3-031-88838-0_17
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