Minimum Contrast Estimation in Fractional Ornstein-Uhlenbeck Driven by Fractional Ornstein-Uhlenbeck Process

Abstract

We generalize fractional Ornstein-Uhlenbeck process whose driving term is another fractional Ornstein-Uhlenbeck process. The motivation is related to stochastic volatility model. We estimate the parameters of both processes by maximum likelihood method and minimum contrast method. We obtain strong consistency and asymptotic normality of the estimators as the time length of observation becomes large. KEYWORDS: Stochastic differential equation, fractional Brownian motion, fractional Ornstein-Uhlenbeck process, correlation, volatility, maximum likelihood estimator, minimum contrast estimator, Durbin-Watson statistic.