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Hidden AR process and adaptive Kalman filter

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  • Yury A. Kutoyants

    (Le Mans University
    International Laboratory “Statistics of Stochastic Processes”, 634050, Tomsk State University)

Abstract

This work discusses a model of a partially observed linear system that depends on some unknown parameters. An approximation of the unobserved component is proposed, which involves three steps. First, a method of moment estimator of unknown parameters is constructed, and second, this estimator is used to define the one-step MLE-process. Finally, the last estimator is substituted into the equations of the Kalman filter. The solution of obtained equations provides us with the desired approximation (adaptive Kalman filter). The asymptotic properties of all the mentioned estimators and both maximum likelihood and Bayesian estimators of the unknown parameters are detailed. The asymptotic efficiency of adaptive filtering is discussed.

Suggested Citation

  • Yury A. Kutoyants, 2025. "Hidden AR process and adaptive Kalman filter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(1), pages 61-103, February.
    • Handle: RePEc:spr:aistmt:v:77:y:2025:i:1:d:10.1007_s10463-024-00908-7
    DOI: 10.1007/s10463-024-00908-7
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    References listed on IDEAS

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    1. Kutoyants, Yury A., 2019. "On parameter estimation of the hidden Ornstein–Uhlenbeck process," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 248-263.
    2. Kutoyants, Yury A., 2024. "Volatility estimation of hidden Markov processes and adaptive filtration," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    3. Jo Thori Lind, 2005. "Repeated surveys and the Kalman filter," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 418-427, December.
    Full references (including those not matched with items on IDEAS)

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