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Fast Filtering and Smoothing for Multivariate State Space Models

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  • Koopman, S.J.M.

    (Tilburg University, School of Economics and Management)

  • Durbin, J.

Abstract

This paper investigates a new approach to diffuse filtering and smoothing for multivariate state space models. The standard approach treats the observations as vectors, while our approach treats each element of the observational vector individually. This strategy leads to computationally efficient methods for multivariate filtering and smoothing. Also, the treatment of the diffuse initial state vector in multivariate models is much simpler than in existing methods. The paper presents details of relevant algorithms for filtering, prediction and smoothing. Proofs are provided. Three examples of multivariate models in statistics and economics are presented for which the new approach is particularly relevant.
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Suggested Citation

  • Koopman, S.J.M. & Durbin, J., 1998. "Fast Filtering and Smoothing for Multivariate State Space Models," Other publications TiSEM 3ca0d14b-21ad-427f-8631-e, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:3ca0d14b-21ad-427f-8631-efb16eb47081
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    References listed on IDEAS

    as
    1. Ralph D. Snyder & Grant R. Saligari, 1996. "Initialization Of The Kalman Filter With Partially Diffuse Initial Conditions," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(4), pages 409-424, July.
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