Berry-Esseen bound for the Parameter Estimation of Fractional Ornstein-Uhlenbeck Processes

Yong Chen, Nenghui Kuang, Ying Li

Published 2018-06-05Version 1

For the least squares estimator $\hat{\theta}$ for the drift parameter $\theta$ of an Ornstein-Uhlenbeck process driven by fractional Brownian motion with Hurst index $H\in [\frac12,\frac34]$, we show the Berry-Esseen bound of the Kolmogorov distance between Gaussian random variable and $\sqrt{T}(\hat{\theta}_T-\theta) $ with $H\in[\frac12,\,\frac34)$, ( $\sqrt{\frac{T}{\log T}}(\hat{\theta}_T-\theta)$ with $H=\frac{3}{4}$ respectively) is $\frac{1}{\sqrt{T^{3-4H}}}$, ( $\frac{1}{\log T}$ respectively). The strategy is to exploit Corollary 1 of Kim and Park [Journal of Multivariate Analysis 155, P284-304.(2017)].