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arXiv · 1902.08500

On Parameter Estimation of Hidden Ergodic Ornstein-Uhlenbeck Process

Yury A. Kutoyants
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Abstract

We consider the problem of parameter estimation for the partially observed linear stochastic differential equation. We assume that the unobserved Ornstein-Uhlenbeck process depends on some unknown parameter and estimate the unobserved process and the unknown parameter simultaneously. We construct the two-step MLE-process for the estimator of the parameter and describe its large sample asymptotic properties, including consistency and asymptotic normality. Using the Kalman-Bucy filtering equations we construct recurrent estimators of the state and the parameter.

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Yury A. Kutoyants. 2019-02-22. On Parameter Estimation of Hidden Ergodic Ornstein-Uhlenbeck Process. https://arxiv.org/abs/1902.08500

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