The mean reverting Ornstein-Uhlenbeck processes with nonlinear autoregressive drift term innovations

Abstract

The main purpose of this paper is to present a new approach for energy markets governed by a two-factor Ornstein-Uhlenbeck process with a stochastic nonlinear autoregressive drift term innovation and an unknown diffusion coefficient. This model has interesting characteristics: since the drift is stochastic, it allows for price to fluctuate around a level that is not fixed. A semiparametric method is proposed to estimate the nonlinear regression function based on the conditional least square method for parametric estimation and the nonparametric kernel approach for the AR adjustment estimation. For estimating the diffusion coefficient of the Ornstein-Uhlenbeck process from discretely observed data a semiparametric approach based on the least-squares estimator is carried out. Finally, numerical simulations are performed using Matlab programming to show efficiency and the accuracy of the present work.