Parameter estimation for fractional Ornstein-Uhlenbeck processes of general Hurst parameter

This paper studies the least squares estimator (LSE) for the drift parameter of an Ornstein-Uhlenbeck process driven by fractional Brownian motion, whose observations can be made either continuously or at discrete time instants. A central limit theorem is proved when the Hurst parameter H is an element of (0, 3/4] and a noncentral limit theorem is proved for H. (3/4, 1). Thus, the open problem left in the previous paper (Hu and Nualart in Stat Probab Lett 80(11-12):1030-1038, 2010) is completely solved, where a central limit theorem for the least squares estimator is proved for H. [1/2, 3/4). The LSE is then used to study the asymptotics for other alternative estimators, such as the ergodic type estimator.