Least squares estimation for the Ornstein-Uhlenbeck process with small Hermite noise

被引：0

作者：

Araya, Hector ^{[1
]}

Torres, Soledad ^{[2
]}

Tudor, Ciprian A. ^{[3
]}

机构：

[1] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Penalolen, Chile

[2] Univ Valparaiso, Fac Ingn, CIMFAV, Inst Ingn Matemat, Valparaiso 2362905, Chile

[3] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

来源：

STATISTICAL PAPERS | 2024年 / 65卷 / 07期

基金：

日本科学技术振兴机构;

关键词：

Non Gaussian; Hermite process; Parameter estimation; Multiple Wiener-It & ocirc; integrals; Ornstein-Uhlenbeck process; Small noise; DIFFERENTIAL-EQUATIONS DRIVEN; PARAMETER-ESTIMATION; DIFFUSIONS; INFERENCE;

D O I：

10.1007/s00362-024-01579-5

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 consider the problem of the drift parameter estimation for a non-Gaussian long memory Ornstein-Uhlenbeck process driven by a Hermite process. To estimate the unknown parameter, discrete time high-frequency observations at regularly spaced time points and the least squares estimation method are used. By means of techniques based on Wiener chaos and multiple stochastic integrals, the consistency and the limit distribution of the least squares estimator of the drift parameter have been established. To show the computational implementation of the obtained results, different simulation examples are given.

引用

页码：4745 / 4766

页数：22

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