International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 905082, 20 pages
http://dx.doi.org/10.1155/2012/905082
Research Article

Asymptotic Normality of a Hurst Parameter Estimator Based on the Modified Allan Variance

Alessandra Bianchi,1 Massimo Campanino,2 and Irene Crimaldi3

1Department of Pure and Applied Mathematics, University of Padua, Via Trieste 63, 35121 Padova, Italy
2Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
3IMT Institute for Advanced Studies, Piazza S. Ponziano 6, 55100 Lucca, Italy

Received 25 July 2012; Revised 9 October 2012; Accepted 21 October 2012

Academic Editor: Hari Srivastava

Copyright © 2012 Alessandra Bianchi 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

In order to estimate the memory parameter of Internet traffic data, it has been recently proposed a log-regression estimator based on the so-called modified Allan variance (MAVAR). Simulations have shown that this estimator achieves higher accuracy and better confidence when compared with other methods. In this paper we present a rigorous study of the MAVAR log-regression estimator. In particular, under the assumption that the signal process is a fractional Brownian motion, we prove that it is consistent and asymptotically normally distributed. Finally, we discuss its connection with the wavelets estimators.