Expectiles for subordinated Gaussian processes with applications

TL;DR

This paper introduces expectile-based estimators for the Hurst exponent of fractional Brownian motion, demonstrating their robustness and asymptotic properties through theoretical analysis and simulations.

Contribution

It presents a novel expectile-based estimation method for the Hurst exponent and establishes its asymptotic properties for subordinated Gaussian processes.

Findings

Expectile estimators are more robust to data rounding than quantile-based methods.

Asymptotic results are derived for expectiles of subordinated Gaussian processes.

Simulation studies confirm the effectiveness of the proposed estimators.

Abstract

In this paper, we introduce a new class of estimators of the Hurst exponent of the fractional Brownian motion (fBm) process. These estimators are based on sample expectiles of discrete variations of a sample path of the fBm process. In order to derive the statistical properties of the proposed estimators, we establish asymptotic results for sample expectiles of subordinated stationary Gaussian processes with unit variance and correlation function satisfying $\rho(i)\sim \kappa|i|^{-\alpha}$ ($\kappa\in \RR$) with $\alpha>0$. Via a simulation study, we demonstrate the relevance of the expectile-based estimation method and show that the suggested estimators are more robust to data rounding than their sample quantile-based counterparts.