Three-‎‎factor‎ mean reverting Ornstein-‎Uhlenbeck‎ process with stochastic drift term innovations‎: ‎Nonlinear autoregressive approach with dependent ‎error

Abstract

This paper investigates a novel approach for energy‎ ‎markets governed by a three-factor mean reverting Ornstein-Uhlenbeck process with a stochastic nonlinear‎ ‎autoregressive drift term by considering dependent error‎. ‎The unique solvability for the given nonlinear system was initially ‎investigated.‎ After that, a semiparametric method based on the conditional least square ‎estimator‎ for the parametric approach and the nonparametric kernel method for autoregressive modification estimation is given to estimate the nonlinear regression function‎‎. ‎Maximum likelihood estimator is used for parameter estimation of the Ornstein-Uhlenbeck process‎. ‎Finally‎, ‎some numerical simulations and real data studies are given to illustrate our main ‎conclusions.‎‎‎