Parameter estimation for the Rosenblatt Ornstein-Uhlenbeck process with periodic mean

Abstract

We study the least squares estimator for the drift parameter of the Langevin stochastic equation driven by the Rosenblatt process. Using the techniques of the Malliavin calculus and the stochastic integration with respect to the Rosenblatt process, we analyze the consistency and the asymptotic distribution of this estimator. We also introduce alternative estimators, which can be simulated, and we study their asymptotic properties.