Estimation of the Hurst Exponent Using Trimean Estimators on Nondecimated Wavelet Coefficients

TL;DR

This paper introduces a robust method for estimating the Hurst exponent using non-decimated wavelet coefficients and trimean estimators, improving accuracy and variance reduction over existing methods.

Contribution

The paper proposes a novel trimean-based estimator for the Hurst exponent that enhances robustness and precision compared to standard wavelet-based estimators.

Findings

Reduces variance of Hurst exponent estimations.

Increases prediction accuracy in high-frequency data.

Effective in classifying visual impairment levels.

Abstract

Hurst exponent is an important feature summarizing the noisy high-frequency data when the inherent scaling pattern cannot be described by standard statistical models. In this paper, we study the robust estimation of Hurst exponent based on non-decimated wavelet transforms (NDWT). The robustness is achieved by applying a general trimean estimator on non-decimated wavelet coefficients of the transformed data. The general trimean estimator is derived as a weighted average of the distribution's median and quantiles, combining the median's emphasis on central values with the quantiles' attention to the extremes. The properties of the proposed Hurst exponent estimators are studied both theoretically and numerically. Compared with other standard wavelet-based methods (Veitch $\&$ Abry (VA) method, Soltani, Simard, $\&$ Boichu (SSB) method, median based estimators MEDL and MEDLA), our methods reduce the variance of the estimators and increase the prediction precision in most cases. The proposed methods are applied to a data set in high frequency pupillary response behavior (PRB) with the goal to classify individuals according to a degree of their visual impairment.