THE MEAN REVERTING ORNSTEIN-UHLENBECK PROCESSES WITH NONLINEAR AUTOREGRESSIVE DRIFT TERM INNOVATIONS

THE MEAN REVERTING ORNSTEIN-UHLENBECK PROCESSES WITH NONLINEAR AUTOREGRESSIVE DRIFT TERM INNOVATIONS

P. Nabati

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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 nonlin- ear autoregressive drift term innovation and an unknown di usion coe cient. This model has interesting characteristics: since the drift is stochastic, it allows for price to uctuate around a level that is not  xed. A semiparametric method is proposed to estimate the nonlinear regression function based on the conditional least square method for paramet- ric estimation and the nonparametric kernel approach for the AR adjustment estimation. For estimating the di usion coe cient 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 e ciency and the accuracy of the present work.

Keywords

Ornstein-Uhlenbeck processes; Nonlinear autoregressive model; Semipara- metric estimation; Smooth kernel approach; Conditional nonlinear least-squares method.