Parameter estimation for the Rosenblatt Ornstein-Uhlenbeck process with periodic mean

被引：7
|
作者：
Shevchenko, Radomyra [1 ]
Tudor, Ciprian A. [2 ,3 ]
机构：
[1] TU Dortmund, LSIV, Fak Math, Vogelpothsweg 87, D-44227 Dortmund, Germany
[2] Univ Lille, CNRS, Lab Paul Painleve, UMR 8524, F-59655 Villeneuve Dascq, France
[3] Romanian Acad, ISMMA, Bucharest, Romania
来源：
STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES | 2020年 / 23卷 / 01期
关键词：
Rosenblatt process; Parameter estimation; Malliavin calculus; Multiple Wiener-Ito integrals; Strong consistency; Asymptotic normality; Ornstein-Uhlenbeck process; Periodic mean function; Least squares estimator; INTEGRALS; RESPECT;
D O I：
10.1007/s11203-019-09200-5
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We study the least squares estimator for the drift parameter of the Langevin stochastic equation driven by the Rosenblatt process. Using the techniques of the Malliavin calculus and the stochastic integration with respect to the Rosenblatt process, we analyze the consistency and the asymptotic distribution of this estimator. We also introduce alternative estimators, which can be simulated, and we study their asymptotic properties.
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页码：227 / 247
页数：21
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