Drift parameter estimation for the noisy Ornstein–Uhlenbeck process driven by a Rosenblatt process

We study the problem of estimating the drift parameter in a (non-ergodic) Ornstein–Uhlenbeck process driven by a Rosenblatt process and observed with additive Gaussian noise. Based on discrete observations, we construct a least squares estimator and a method-of-moments-type estimator for the drift. Under suitable conditions, we prove that both procedures are consistent in probability, even in the presence of measurement error. A Monte Carlo simulation study illustrates the finite-sample performance of the estimators under various long-memory regimes.