Fast Filtering and Smoothing for Multivariate State Space Models

S.J.M. Koopman, J. Durbin

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This paper gives 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 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.
Original languageEnglish
Place of PublicationTilburg
Number of pages20
Publication statusPublished - 1998

Publication series

NameCentER Discussion Paper


  • Diffuse initialisation
  • Kalman filter
  • multivariate models
  • smoothing
  • state space
  • time series


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