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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 323091, 7 pages
http://dx.doi.org/10.1155/2014/323091
Research Article

Asymptotic Normality of the Estimators for Fractional Brownian Motions with Discrete Data

1School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
2School of Economics and Commerce, South China University of Technology, Guangzhou 510006, China
3School of Business Administration, South China University of Technology, Guangzhou 510640, China

Received 13 November 2013; Accepted 4 January 2014; Published 23 February 2014

Academic Editor: Weilin Xiao

Copyright © 2014 Lin Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with the problem of estimating the Hurst parameter in the fractional Brownian motion when the Hurst index is greater than one half. The estimation procedure is built upon the marriage of the autocorrelation approach and the maximum likelihood approach. The asymptotic properties of the estimators are presented. Using the Monte Carlo experiments, we compare the performance of our method to existing ones, namely, R/S method, variations estimators, and wavelet method. These comparative results demonstrate that the proposed approach is effective and efficient.