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On parameter estimation of the hidden Ornstein–Uhlenbeck process

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  • Kutoyants, Yury A.

Abstract

This paper considers parameter estimation in the Ornstein–Uhlenbeck process observed in the presence of Gaussian white noise. We show the consistency and asymptotic normality of the maximum likelihood estimator in small-noise asymptotics. The data are assumed to arise from a non-homogeneous partially observed linear system. The construction and study of the estimator are based mainly on the asymptotics of the equations of Kalman–Bucy filtration.

Suggested Citation

  • Kutoyants, Yury A., 2019. "On parameter estimation of the hidden Ornstein–Uhlenbeck process," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 248-263.
    • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:248-263
    DOI: 10.1016/j.jmva.2018.09.008
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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, Yu.A., 2017. "On the multi-step MLE-process for ergodic diffusion," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2243-2261.
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    Cited by:

    1. Karol Binkowski & Peilun He & Nino Kordzakhia & Pavel Shevchenko, 2021. "On the Parameter Estimation in the Schwartz-Smiths Two-Factor Model," Papers 2108.01881, arXiv.org.
    2. Peilun He & Karol Binkowski & Nino Kordzakhia & Pavel Shevchenko, 2021. "On Modelling of Crude Oil Futures in a Bivariate State-Space Framework," Papers 2108.01886, arXiv.org.
    3. Peilun He & Karol Binkowski & Nino Kordzakhia & Pavel Shevchenko, 2021. "On Modelling of Crude Oil Futures in a Bivariate State-Space Framework," Springer Books, in: Marco Corazza & Manfred Gilli & Cira Perna & Claudio Pizzi & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 273-278, Springer.
    4. Masahiro Kurisaki, 2023. "Parameter estimation for ergodic linear SDEs from partial and discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 279-330, July.
    5. Yury A. Kutoyants, 2021. "On localization of source by hidden Gaussian processes with small noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 671-702, August.

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