Asymptotic expansion of an estimator for the Hurst coefficient

TL;DR

This paper derives an asymptotic expansion for an estimator of the Hurst coefficient in fractional Brownian motion, using advanced Wiener functional theory, and demonstrates its effectiveness through numerical experiments.

Contribution

It introduces a novel asymptotic expansion approach for the Hurst coefficient estimator utilizing recent Wiener functional theory.

Findings

Asymptotic expansion improves estimator accuracy.

Numerical studies validate theoretical results.

Enhanced understanding of estimator distribution.

Abstract

Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. For this, a recently developed theory of asymptotic expansion of the distribution of Wiener functionals is applied. The effects of the asymptotic expansion are demonstrated by numerical studies.