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Reconstructing the Kalman Filter for Stationary and Non Stationary Time Series

Author

Listed:
  • Snyder Ralph D

    (Monash University)

  • Forbes Catherine S

    (Monash University)

Abstract

A Kalman filter for application to stationary or non-stationary time series is proposed. A major feature is a new initialisation method to accommodate non-stationary time series. The filter works on time series with missing values at any point of time including the initialisation phase. It can also be used where a state space model does not satisfy the traditional observability condition, a situation that can arise with seasonal time series.Another feature of the paper is that the Kalman filter is described in terms of the augmented moments of the state vectors, these being an aggregate of means, variances, covariances and other pertinent information. By doing this, the Kalman filter is specified without direct recourse to those relatively complex formulae for calculating associated means and variances found in traditional expositions.A computer implementation of the Kalman filter is also described where the augmented moments are treated as an object; the operations of addition and multiplication are overloaded to work on instances of this object; and a form of statistical conditioning is implemented as an operator.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:sndecm:v:7:y:2003:i:2:n:al1
    DOI: 10.2202/1558-3708.1087
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    References listed on IDEAS

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    1. Everette S. Gardner, Jr. & Ed. Mckenzie, 1985. "Forecasting Trends in Time Series," Management Science, INFORMS, vol. 31(10), pages 1237-1246, October.
    2. 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.
    3. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737.
    4. 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.
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    Cited by:

    1. Rob Hyndman & Muhammad Akram & Blyth Archibald, 2008. "The admissible parameter space for exponential smoothing models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 407-426, June.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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