A short note on a class of statistics for estimation of the Hurst index of fractional Brownian motion

TL;DR

This paper introduces a new class of statistics based on second order increments for estimating the Hurst index of fractional Brownian motion from discrete observations.

Contribution

It proposes a novel statistical approach specifically designed for accurate Hurst index estimation using second order increments.

Findings

New class of statistics suitable for Hurst index estimation

Method demonstrated on discrete fractional Brownian motion data

Potential for improved estimation accuracy

Abstract

We propose some class of statistics suitable for estimation of the Hurst index of the fractional Brownian motion based on the second order increments of an observed discrete trajectory.