Parameter estimation for fractional Ornstein–Uhlenbeck processes

Abstract: We study a least squares estimator for the Ornstein–Uhlenbeck process, , driven by fractional Brownian motion with Hurst parameter . We prove the strong consistence of (the almost surely convergence of to the true parameter ). We also obtain the rate of this convergence when , applying a central limit theorem for multiple Wiener integrals. This least squares estimator can be used to study other more simulation friendly estimators such as the estimator obtained by a function of . [Copyright &y& Elsevier]