Least squares estimator of Ornstein-Uhlenbeck processes driven by fractional Lévy processes with periodic mean

Abstract

We deal with the least squares estimator for the drift parameters of an Ornstein-Uhlenbeck process with periodic mean function driven by fractional Lévy process. For this estimator, we obtain consistency and the asymptotic distribution. Compared with fractional Ornstein-Uhlenbeck and Ornstein-Uhlenbeck driven by Lévy process, they can be regarded both as a Lévy generalization of fractional Brownian motion and a fractional generaliza- tion of Lévy process.

Keywords

Least squares estimator / Ornstein-Uhlenbeck processes / fractional Lévy processes / asymptotic distribution

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