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Volatility estimation of hidden Markov processes and adaptive filtration

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  • Kutoyants, Yury A.

Abstract

The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. The coefficients of this system are supposed to depend on some unknown parameter. The problem of estimation of these parameters is considered and the possibility of the approximation of the filtering equations is discussed. An estimators are used for estimation of the quadratic variation of the derivative of the limit of the observed process. Then this estimator is used for nonparametric estimation of the integral of the square of volatility of unobservable component. This estimator is also used for construction of method of moments estimators in the case where the drift in observable component and the volatility of the state component depend on some unknown parameter. Then this method of moments estimator and Fisher-score device allow us to introduce the One-step MLE-process and adaptive Kalman–Bucy filter. The asymptotic efficiency of the proposed filter is discussed.

Suggested Citation

  • Kutoyants, Yury A., 2024. "Volatility estimation of hidden Markov processes and adaptive filtration," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:spapps:v:173:y:2024:i:c:s0304414924000875
    DOI: 10.1016/j.spa.2024.104381
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    References listed on IDEAS

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    1. Pavel Chigansky, 2009. "Maximum likelihood estimator for hidden Markov models in continuous time," Statistical Inference for Stochastic Processes, Springer, vol. 12(2), pages 139-163, June.
    2. Kutoyants, Yury A., 2019. "On parameter estimation of the hidden Ornstein–Uhlenbeck process," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 248-263.
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