JSM 2005 - Toronto

Abstract #302532

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Activity Number: 462
Type: Invited
Date/Time: Thursday, August 11, 2005 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #302532
Title: Wavelet-based Convex Rearrangements in Estimation of Hurst Exponent
Author(s): Brani Vidakovic*+
Companies: Georgia Institute of Technology
Address: School of Industrial and Systems Engineering, Atlanta, GA, 30332,
Keywords: Hurst Exponent ; Selfsimilar Process ; Convex Rearrangements ; Wavelets ; Fractional Brownian Motion
Abstract:

In this paper, an estimator of Hurst exponent in a monofractal, self-similar process is proposed. The estimator utilizes the convex rearrangements of properly wavelet-filtered versions of the process. This work builds on the research of Davydov, Thilly, Phillippe, and Coeurjolly, who investigated the asymptotic behavior of normalized convex rearrangements for broad classes of Gaussian and alpha-stable processes. We define G-convex rearrangements where G is a filter belonging to a family of dilated, high-pass wavelet filters. Next, we propose an estimator of Hurst exponent via a ratio of G-convex rearrangements with different dilations. Almost sure convergence and asymptotic distributional properties of the proposed estimator are presented. Extensive simulational analysis compares the proposed estimator to several popular estimators in the field.

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