On Estimation of Hurst Scaling Exponent through Discrete Wavelets

TL;DR

This paper investigates how discrete wavelet coefficients, especially from the Daubechies family, can accurately estimate the Hurst scaling exponent in non-stationary time series across various data sets.

Contribution

It demonstrates that discrete wavelet-based fluctuation functions effectively estimate the Hurst exponent, comparing favorably with continuous wavelet methods.

Findings

High-pass Daubechies wavelet coefficients accurately estimate fluctuation power.

Discrete wavelet methods reliably determine Hurst exponents in non-stationary data.

Comparison shows advantages over continuous wavelet approaches.

Abstract

We study the scaling behavior of the fluctuations, as extracted through wavelet coefficients based on discrete wavelets. The analysis is carried out on a variety of physical data sets, as well as Gaussian white noise and binomial multi-fractal model time series and the results are compared with continuous wavelet based average wavelet coefficient method. It is found that high-pass coefficients of wavelets, belonging to the Daubechies family are quite good in estimating the true power in the fluctuations in a non-stationary time series. Hence, the fluctuation functions based on discrete wavelet coefficients find the Hurst scaling exponents accurately.