Asymptotically efficient estimation of Ergodic rough fractional Ornstein-Uhlenbeck process under continuous observations

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 asymp...

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Bibliographic Details
Published inStatistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems Vol. 27; no. 1; pp. 103 - 122
Main Authors Chiba, Kohei, Takabatake, Tetsuya
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2024
Springer Nature B.V
Subjects
Asymptotic properties
Drift estimation
Ergodic processes
Mathematics
Mathematics and Statistics
Maximum likelihood estimators
Ornstein-Uhlenbeck process
Parameters
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Estimation of drift parameters
Fractional Ornstein-Uhlenbeck process
Continuous observations
Local asymptotic normality property
62M09
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Summary: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.
ISSN:1387-0874
1572-9311
DOI:10.1007/s11203-023-09300-3