Frequency-Domain Estimation of Continuous-Time Bilinear Processes

In this paper, we study in frequency domain some probabilistic and statistical properties of continuous-time version of the well-known bilinear processes driven by a standard Brownian motion. This class of processes which encompasses many commonly used processes in the literature was defined as a nonlinear stochastic differential equation which has raised considerable interest in the last few years. So, the L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {L}}_{2}$$\end{document}-structure of the process is studied and its covariance function is given. These structures will lead to study the strong consistency and asymptotic normality of the Whittle estimates of the unknown parameters involved in the process. Finite sample properties are also considered through Monte Carlo experiments. In end, the model is then used to model the exchanges rate of the Algerian Dinar against the US dollar.