ARCH model and fractional Brownian motion

被引：5

作者：

Bahamonde, Natalia ^{[1
]}

Torres, Soledad ^{[2
]}

Tudor, Ciprian A. ^{[2
,3
]}

机构：

[1] Pontificia Univ Catolica Valparaiso, Inst Estadist, Valparaiso, Chile

[2] Univ Valparaiso, Fac Ingn, CIMFAV, Valparaiso, Chile

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

来源：

STATISTICS & PROBABILITY LETTERS | 2018年 / 134卷

关键词：

ARCH model; Fractional Brownian motion; Stationary process; Volatility;

D O I：

10.1016/j.spl.2017.10.003

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 an extension of the ARCH model that includes the squared fractional Brownian motion. We study the statistical properties of the model as the conditions for the existence of a stationary solution and the moments of the process. We study their asymptotic behavior of the autocorrelation function of the squared of the process and we prove that the long memory property of the model holds. We illustrate our results by numerical simulations. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：70 / 78

页数：9

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