Determination of the Hurst Exponent by Use of Wavelet Transforms

TL;DR

This paper introduces a wavelet-based method for accurately estimating the Hurst exponent, especially effective with limited data samples, outperforming traditional Fourier spectral analysis in such scenarios.

Contribution

The paper presents a novel wavelet-based approach for Hurst exponent determination that improves accuracy with small sample sizes compared to Fourier methods.

Findings

Wavelet method outperforms Fourier analysis with few samples.

Both methods are comparable with many samples.

Method effective on synthetic, fracture, and economic data.

Abstract

We propose a new method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces and data from economy. The results are compared with those obtained from Fourier spectral analysis. When many samples are available, the wavelet and Fourier methods are comparable in accuracy. However, when one or only a few samples are available, the wavelet method outperforms the Fourier method by a large margin.