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

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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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  -