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Note On The Kalman Filter With Estimated Parameters

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  • N. Watanabe

Abstract

. State estimation and prediction problems are considered for a stochastic process represented by a state space form which involves unknown parameters. We first study the stability of the Kalman filter corresponding to the state space form without assuming the stationarity of the process. Second, we consider the state estimation and prediction when the process is stationary, and show some asymptotic properties of the state estimates and predicted values obtained by the Kalman filter with estimated parameters which converge to the true parameters or to the equivalent classes of the true parameters with probability one.

Suggested Citation

  • N. Watanabe, 1985. "Note On The Kalman Filter With Estimated Parameters," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(4), pages 269-278, July.
    • Handle: RePEc:bla:jtsera:v:6:y:1985:i:4:p:269-278
    DOI: 10.1111/j.1467-9892.1985.tb00415.x
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    Cited by:

    1. Cavanaugh, Joseph E. & Shumway, Robert H., 1996. "On computing the expected Fisher information matrix for state-space model parameters," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 347-355, March.
    2. Danny Pfeffermann & Richard Tiller, 2005. "Bootstrap Approximation to Prediction MSE for State–Space Models with Estimated Parameters," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 893-916, November.
    3. Tusell Palmer, Fernando Jorge, 2005. "Multiple imputation of time series: an application to the construction of historical price indexes," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).

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