Asymptotically Efficient Estimation of Ergodic Rough Fractional Ornstein-Uhlenbeck Process under Continuous Observations

2022/04/07 by Kohei Chiba, Chiba, Kohei, Tetsuya Takabatake +1
Economics, Econometrics and Finance · Mathematics · Decision Sciences · #Stochastic processes and financial applications #Statistical Methods and Inference #Advanced Statistical Process Monitoring

paper · pdf · doi:10.48550/arxiv.2204.03271

Abstract

We consider the problem of asymptotically efficient estimation of drift parameters of the ergodic fractional Ornstein-Uhlenbeck process under continuous observations when the Hurst parameter H<1/2 and the mean of its stationary distribution is not equal to zero. In this paper, we derive asymptotically efficient rates and variances of estimators of drift parameters and prove an asymptotic efficiency of a maximum likelihood estimator of drift parameters.

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