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

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.