Journal of Statistical Theory and Applications

Volume 17, Issue 4, December 2018, Pages 606 - 615

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

Authors
Abdelouahab Bibi1, Fateh Merahi2, *
1Department of Mathematics, UMC(1), Constantine, Algeria
2Department of Mathematics, UMC(1), Constantine, Algeria
*

Corresponding author. Email: merahfateh@yahoo.fr

Received 18 March 2017, Accepted 15 November 2017, Available Online 31 December 2018.
DOI
10.2991/jsta.2018.17.4.3How to use a DOI?
Keywords
Continuous-time bilinear process; Fractional movement Brownian; Spectral representation; Itô's solution; Long memory property.
Abstract

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 Itô'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.

Copyright
© 2018 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

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Journal
Journal of Statistical Theory and Applications
Volume-Issue
17 - 4
Pages
606 - 615
Publication Date
2018/12/31
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
10.2991/jsta.2018.17.4.3How to use a DOI?
Copyright
© 2018 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Abdelouahab Bibi
AU  - Fateh Merahi
PY  - 2018
DA  - 2018/12/31
TI  - A Study of the First-Order Continuous-Time Bilinear Processes Driven by Fractional Brownian Motion
JO  - Journal of Statistical Theory and Applications
SP  - 606
EP  - 615
VL  - 17
IS  - 4
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2018.17.4.3
DO  - 10.2991/jsta.2018.17.4.3
ID  - Bibi2018
ER  -