Optimal filtering equations in state space model of the two factors mean reverting Ornstein-Uhlenbech process

Abstract

This paper investigates a nonlinear state space model for energy markets ruled by a two factor mean reverting Ornstein Uhlenbeck process with a stochastic nonlinear autoregressive drift term. A recursive approach using Taylor series based approximations for filtering, prediction, and smoothing problem of the hidden mean reverting factor from the noisy observations is proposed. The closed-form solutions are obtained for estimating the hidden mean reverting factor. Also, the existence and uniqueness of the solution for this nonlinear system are proved. Finally, the performance of the developed methods is checked in a simulation study.

Keywords:

• Ornstein Uhlenbeck process
• state space model
• estimation of the hidden mean reverting factor
• optimal filtering equations