Least squares estimator of fractional Ornstein-Uhlenbeck processes with periodic mean

被引：22

作者：

Bajja, Salwa ^{[1
]}

Es-Sebaiy, Khalifa ^{[1
]}

Viitasaari, Lauri ^{[2
]}

机构：

[1] Cadi Ayyad Univ, Natl Sch Appl Sci Marrakesh, Marrakech, Morocco

[2] Aalto Univ, Sch Sci, Dept Math & Syst Anal, POB 11100, FIN-00076 Aalto, Finland

来源：

JOURNAL OF THE KOREAN STATISTICAL SOCIETY | 2017年 / 46卷 / 04期

关键词：

Fractional Ornstein-Uhlenbeck processes; Least squares estimator; Malliavin calculus; PARAMETER-ESTIMATION;

D O I：

10.1016/j.jkss.2017.06.002

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 first study the drift parameter estimation of the fractional Ornstein-Uhlenbeck process (fOU) with periodic mean for every 1/2 < H < 1, More precisely, we extend the consistency proved in Dehling et al. (2016) for 1/2 < H < 3/4 to the strong consistency for any 1/2 < H < 1 on the one hand, and on the other, we also discuss the asymptotic normality given in Dehling et al. (2016). In the second main part of the paper, we study the strong consistency and the asymptotic normality of the fOU of the second kind with periodic mean for any 1/2 < H < 1. (C) 2017 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

引用

页码：608 / 622

页数：15

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