Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles

2005/06/15 by Jean-François Coeurjolly, Jean‐François Coeurjolly, Coeurjolly, Jean-François · 2 citations
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling #Mathematical Dynamics and Fractals #math.ST #msc:60G18 #msc:62G30 #stat.TH

paper · pdf · doi:10.48550/arxiv.math/0506290

44 pages, février 2007

arxiv created 2007/02/08 · arxiv updated 2009/12/01

Abstract

This paper is devoted to the introduction of a new class of consistent estimators of the fractal dimension of locally self-similar Gaussian processes. These estimators are based on convex combinations of sample quantiles of discrete variations of a sample path over a discrete grid of the interval [0,1]. We derive the almost sure convergence and the asymptotic normality for these estimators. The key-ingredient is a Bahadur representation for sample quantiles of non-linear functions of Gaussians sequences with correlation function decreasing as k^-αL(k) for some α>0 and some slowly varying function L(⋅).

Citations

• Fractional Brownian Motions, Fractional Noises and Applications

Cited by

• A Noise Resilient Approach for Robust Hurst Exponent Estimation
• On the passage times of self-similar Gaussian processes on curved boundaries

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