Parameter identification for fractional Ornstein–Uhlenbeck processes based on discrete observation

Abstract

Fractional Ornstein–Uhlenbeck process is an extended model of the traditional Ornstein–Uhlenbeck process that provides some useful models for many physical and financial phenomena demonstrating long-range dependencies. Obviously, if some phenomenon can be modeled by fractional Ornstein–Uhlenbeck processes, the problem of estimating unknown parameters in these models is of great interest, especially, in discrete time. This paper deals with the problem of estimating the unknown parameters in fractional Ornstein–Uhlenbeck processes. The estimation procedure is built upon the marriage of the quadratic variation method and the maximum likelihood approach. The consistency of these estimators is also provided. Simulation outcomes illustrate that our methodology is efficient and reliable.