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On Parameter Estimation of Hidden Ergodic Ornstein-Uhlenbeck Process (1902.08500v1)
Published 22 Feb 2019 in math.ST and stat.TH
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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