Exact confidence intervals for the Hurst parameter of a fractional Brownian motion

DOI10.1214/09-EJS366zbMath1326.62065arXiv0901.4456MaRDI QIDQ1951985

Jean-Christophe Breton, Ivan Nourdin, Giovanni Peccati

Publication date: 27 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.4456

zbMATH Keywords

fractional Brownian motionHurst parameterconcentration inequalitiesexact confidence intervals

Mathematics Subject Classification ID

Parametric tolerance and confidence regions (62F25) Gaussian processes (60G15) Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (15)

Stokes formula on the Wiener space and \(n\)-dimensional Nourdin-Peccati analysis ⋮ Unnamed Item ⋮ The Hurst phenomenon and the rescaled range statistic ⋮ Exact confidence intervals of the extended Orey index for Gaussian processes ⋮ A Baxter type estimator of an unknown parameter of the covariance function in the non-Gaussian case ⋮ On Hölder fields clustering ⋮ Convergence rate of CLT for the estimation of Hurst parameter of fractional Brownian motion ⋮ Remarks on confidence intervals for self-similarity parameter of a subfractional Brownian motion ⋮ Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size ⋮ Forecasting of time data with using fractional Brownian motion ⋮ On some estimators of the Hurst index of the solution of SDE driven by a fractional Brownian motion ⋮ The rate of convergence of Hurst index estimate for the stochastic differential equation ⋮ Variance Estimation for Fractional Brownian Motions with Fixed Hurst Parameters ⋮ Cumulants on the Wiener space ⋮ Malliavin Calculus and Self Normalized Sums

Uses Software

• longmemo

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stein's method on Wiener chaos
• Variations and estimators for self-similarity parameters via Malliavin calculus
• Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion
• Density formula and concentration inequalities with Malliavin calculus
• Central limit theorems for non-linear functionals of Gaussian fields
• Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series
• Absolute continuity of probability laws of Wiener functionals
• Quadratic variations and estimation of the local Hölder index of a Gaussian process
• Edgeworth expansions for semiparametric Whittle estimation of long memory.
• Central limit theorems for multiple stochastic integrals and Malliavin calculus
• The Malliavin Calculus and Related Topics
• Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths

This page was built for publication: Exact confidence intervals for the Hurst parameter of a fractional Brownian motion