Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size

2009/10/16 by Jean-Christophe Breton, Breton, Jean-Christophe, Jean‐François Coeurjolly +1
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.0910.3088

openalex publication_date 2009/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose exact confidence intervals of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the fractional Brownian motion is known or unknown are investigated. These intervals are obtained by observing a single discretized sample path of a fractional Brownian motion and without any assumption on the parameter H.

Citations

• Orthonormal bases of compactly supported wavelets

Related

• Exact confidence intervals for the Hurst parameter of a fractional Brownian motion
• On some estimators of the Hurst index of the solution of SDE driven by a fractional Brownian motion
• Fractional Brownian motion and asymptotic Bayesian estimation
• A short note on a class of statistics for estimation of the Hurst index of fractional Brownian motion
• Hurst index estimation in stochastic differential equations driven by fractional Brownian motion