Volatility estimation of hidden Markov processes and adaptive filtration

Yury A. Kutoyants

Stochastic Processes and their Applications, 2024, vol. 173, issue C

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.

Keywords: Hidden Markov processes; Adaptive filtration; Quadratic variation estimation; Nonparametric estimation; Volatility estimation (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2024.104381

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