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Fast Filtering and Smoothing for Multivariate State Space Models


  • S. J. Koopman
  • J. Durbin


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.

Suggested Citation

  • S. J. Koopman & J. Durbin, 2000. "Fast Filtering and Smoothing for Multivariate State Space Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(3), pages 281-296, May.
  • Handle: RePEc:bla:jtsera:v:21:y:2000:i:3:p:281-296

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    Cited by:

    1. Koopman, S.J.M. & Lai, H.N., 1998. "Modelling bid-ask spreads in competitive dealership markets," Discussion Paper 1998-032, Tilburg University, Center for Economic Research.
    2. Snyder Ralph D & Forbes Catherine S, 2003. "Reconstructing the Kalman Filter for Stationary and Non Stationary Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(2), pages 1-20, July.
    3. Borus Jungbacker & Siem Jan Koopman & Michel Wel, 2014. "Smooth Dynamic Factor Analysis With Application To The Us Term Structure Of Interest Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(1), pages 65-90, January.
    4. António Alberto Santos, 2010. "MCMC, likelihood estimation and identifiability problems in DLM models," GEMF Working Papers 2010-12, GEMF, Faculty of Economics, University of Coimbra.
    5. Maarten Dossche & Gerdie Everaert, 2005. "Measuring inflation persistence: a structural time series approach," Working Paper Research 70, National Bank of Belgium.
    6. Cecilia Frale, "undated". "Do Surveys Help in Macroeconomic Variables Disaggregation and Estimation?," Working Papers wp2008-2, Department of the Treasury, Ministry of the Economy and of Finance.
    7. Ingvar Strid & Karl Walentin, 2009. "Block Kalman Filtering for Large-Scale DSGE Models," Computational Economics, Springer;Society for Computational Economics, vol. 33(3), pages 277-304, April.
    8. Proietti, Tommaso, 2008. "Estimation of Common Factors under Cross-Sectional and Temporal Aggregation Constraints: Nowcasting Monthly GDP and its Main Components," MPRA Paper 6860, University Library of Munich, Germany.

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