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

TL;DR

This paper investigates the estimation of the drift parameter in a Langevin equation driven by the Rosenblatt process, analyzing estimator properties using advanced stochastic calculus techniques.

Contribution

It introduces and analyzes the consistency and asymptotic behavior of least squares and alternative estimators for the Rosenblatt-driven Langevin equation.

Findings

Least squares estimator is consistent.

Asymptotic normality of the estimator is established.

Alternative estimators are proposed and their properties studied.

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.