A Study of the First-Order Continuous-Time Bilinear Processes Driven by Fractional Brownian Motion

被引：0

作者：

Bibi, Abdelouahab ^{[1
]}

Merahi, Fateh ^{[1
]}

机构：

[1] UMC 1, Dept Math, Constantine 1, Algeria

来源：

JOURNAL OF STATISTICAL THEORY AND APPLICATIONS | 2018年 / 17卷 / 04期

关键词：

Continuous-time bilinear process; Fractional movement Brownian; Spectral representation; Ito's solution; Long memory property;

D O I：

10.2991/jsta.2018.17.4.3

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：

The continuous-time bilinear (COBL) process has been used to model non linear and/or non Gaussian datasets. In this paper, the first-order continuous-time bilinear COBL (1, 1) model driven by a fractional Brownian motion (fBm for short) process is presented. The use of fBm processes with certain Hurst parameter permits to obtain a much richer class of possibly long-range dependent property which are frequently observed in financial econometrics, and thus can be used as a power tool for modelling irregularly series having memory. So, the existence of Ito's solutions and there chaotic spectral representations for time-varying COBL (1, 1) processes driven by fBm are studied. The second-order properties of such solutions are analyzed and the long-range dependency property are studied. (C) 2018 The Authors. Published by Atlantis Press SARL.

引用

页码：606 / 615

页数：10

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