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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| Published in | Statistical 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 |
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| Language | English |
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01.04.2024
Springer Nature B.V |
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| 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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Takabatake, Tetsuya Chiba, Kohei |
| Author_xml | – sequence: 1 givenname: Kohei surname: Chiba fullname: Chiba, Kohei organization: Graduate School of Engineering Science, Osaka University – sequence: 2 givenname: Tetsuya orcidid: 0000-0002-8734-0459 surname: Takabatake fullname: Takabatake, Tetsuya email: tkbtk@hiroshima-u.ac.jp organization: School of Economics, Hiroshima University |
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| Cites_doi | 10.1007/s11203-020-09214-4 10.3150/18-BEJ1039 10.1111/mafi.12354 10.1080/14697688.2015.1099717 10.1023/A:1021220818545 10.1007/s11203-009-9035-x 10.1214/17-AOS1611 10.1214/009053606000001541 10.1007/s11203-018-9181-0 10.15388/LJS.2017.13674 10.1016/S0304-4149(02)00155-2 10.1525/9780520325883-012 10.1214/EJP.v8-125 10.1007/978-1-4471-3866-2 10.1080/14697688.2017.1393551 10.3390/econometrics8030032 10.1016/j.jeconom.2021.08.001 10.1525/9780520325883-015 10.1017/CBO9781139084659 |
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| Keywords | Estimation of drift parameters Fractional Ornstein-Uhlenbeck process Continuous observations Local asymptotic normality property 62M09 |
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| References | Brouste, Kleptsyna (CR3) 2010; 13 Brouste, Masuda (CR4) 2018; 21 Fukasawa, Takabatake, Westphal (CR8) 2022; 32 CR5 CR19 CR17 Tudor, Viens (CR20) 2007; 35 Bayer, Friz, Gatheral (CR1) 2016; 16 CR9 CR16 Fukasawa, Takabatake (CR7) 2019; 25 CR14 Kleptsyna, Le Breton (CR12) 2002; 5 CR13 CR11 CR10 CR21 Brouste, Fukasawa (CR2) 2018; 46 Chiba (CR6) 2020; 23 Lohvinenko, Ralchenko (CR15) 2017; 56 Nualart, Ouknine (CR18) 2002; 102 CA Tudor (9300_CR20) 2007; 35 M Fukasawa (9300_CR8) 2022; 32 C Bayer (9300_CR1) 2016; 16 M Kleptsyna (9300_CR12) 2002; 5 A Brouste (9300_CR2) 2018; 46 A Brouste (9300_CR4) 2018; 21 K Chiba (9300_CR6) 2020; 23 9300_CR13 9300_CR14 S Lohvinenko (9300_CR15) 2017; 56 9300_CR11 A Brouste (9300_CR3) 2010; 13 9300_CR10 9300_CR21 D Nualart (9300_CR18) 2002; 102 9300_CR19 9300_CR5 9300_CR17 M Fukasawa (9300_CR7) 2019; 25 9300_CR9 9300_CR16 |
| References_xml | – ident: CR21 – volume: 23 start-page: 319 year: 2020 end-page: 353 ident: CR6 article-title: An M-estimator for stochastic differential equations driven by fractional Brownian motion with small Hurst parameter publication-title: Stat Inference Stoch Process doi: 10.1007/s11203-020-09214-4 contributor: fullname: Chiba – ident: CR19 – volume: 25 start-page: 1870 issue: 3 year: 2019 end-page: 1900 ident: CR7 article-title: Asymptotically efficient estimators for self-similar stationary Gaussian noises under high frequency observations publication-title: Bernoulli doi: 10.3150/18-BEJ1039 contributor: fullname: Takabatake – volume: 32 start-page: 1086 issue: 4 year: 2022 end-page: 1132 ident: CR8 article-title: Consistent estimation for fractional stochastic volatility model under high-frequency asymptotics publication-title: Math Finance doi: 10.1111/mafi.12354 contributor: fullname: Westphal – volume: 16 start-page: 887 issue: 6 year: 2016 end-page: 904 ident: CR1 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| SubjectTerms | 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 |
| Title | Asymptotically efficient estimation of Ergodic rough fractional Ornstein-Uhlenbeck process under continuous observations |
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