Local estimation of the Hurst index of multifractional Brownian motion by Increment Ratio Statistic method

TL;DR

This paper develops a method to estimate the time-varying Hurst index of multifractional Brownian motion using Increment Ratio Statistics, supported by theoretical proofs and simulation results.

Contribution

It introduces a new CLT for the Increment Ratio Statistic of multifractional Brownian motion and proposes a simple, effective estimation approach.

Findings

The estimator fits well in simulation studies

Theoretical CLT established for the Hurst index

Method relies on Breuer-Major theorems and a novel freezing strategy

Abstract

We investigate here the Central Limit Theorem of the Increment Ratio Statistic of a multifractional Brownian motion, leading to a CLT for the time varying Hurst index. The proofs are quite simple relying on Breuer-Major theorems and an original freezing of time strategy. A simulation study shows the goodness of fit of this estimator.