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.2010 AMS Classification Numbers: 60H15, 60H07, 60G35.

Parameter Estimation for an Ornstein-Uhlenbeck Process Driven by a General Gaussian Noise

“…MLE was studied in [13], [14] and the limiting distribution is Cauchy for the Brownian motion case, and the LSE in the case of fractional Brownian motion and other Gaussian processes was considered in [15], [16], [17], [18] and the references therein. We also mention some work for the Ornstein-Uhlenbeck process driven by the non-Gaussian Hermite processes with periodic mean in [19], [20] and the references therein.…”

Statistical analysis of the non-ergodic fractional Ornstein-Uhlenbeck process with periodic mean

“…Also, some non-Gaussian extensions of the model (1.1) have been considered by several authors (see e.g. [21,24]), by replacing the fBm in (1.1) by a Hermite process. On the other hand, for p = 1 and φ 1 = 1, a large number of research articles considered the problem of drift parameter estimation for various fractional diffusions and in particular for the fOU process, we refer among many others to [15,14,9,13,7,25].…”