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

摘要

This paper provides several statistical estimators for the drift andvolatility parameters of an Ornstein-Uhlenbeck process driven by fractionalBrownian motion, whose observations can be made either continuously or atdiscrete time instants. First and higher order power variations are used toestimate the volatility parameter. The almost sure convergence of theestimators and the corresponding central limit theorems are obtained for allthe Hurst parameter range $H\in (0, 1)$. The least squares estimator is usedfor the drift parameter. A central limit theorem is proved when the Hurstparameter $H \in (0, 1/2)$ and a noncentral limit theorem is proved for$H\in[3/4, 1)$. Thus, the open problem left in the paper by Hu and Nualart(2010) is completely solved, where a central limit theorem for least squaresestimator is proved for $H\in [1/2, 3/4)$.