Estimating Drift Parameters in a Fractional Ornstein Uhlenbeck Process with Periodic Mean

TL;DR

This paper develops a least squares estimator for drift parameters in a fractional Ornstein-Uhlenbeck process with periodic mean, demonstrating its consistency and asymptotic normality with a convergence rate depending on the Hurst parameter.

Contribution

It introduces a novel estimator for the fractional Ornstein-Uhlenbeck process with periodic mean, analyzing its statistical properties and convergence rate.

Findings

Estimator is consistent and asymptotically normal.

Convergence rate is slower, depending on the Hurst parameter H.

Results extend classical models to include periodic mean functions.

Abstract

We construct a least squares estimator for the drift parameters of a fractional Ornstein Uhlenbeck process with periodic mean function and long range dependence. For this estimator we prove consistency and asymptotic normality. In contrast to the classical fractional Ornstein Uhlenbeck process without periodic mean function the rate of convergence is slower depending on the Hurst parameter $H$, namely $n^{1-H}$.