The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion

TL;DR

This paper introduces a novel method using visibility graphs to accurately estimate the Hurst exponent in fractional Brownian motion, providing a reliable alternative to traditional techniques.

Contribution

It demonstrates that the degree distribution of visibility graphs from fBm series linearly relates to the Hurst parameter, enabling a new approach for analyzing long-range dependence.

Findings

Degree distribution exponent depends linearly on H

Method validated through extensive simulations

Applied to human gait dynamics to quantify persistence

Abstract

Fractional Brownian motion (fBm) has been used as a theoretical framework to study real time series appearing in diverse scientific fields. Because its intrinsic non-stationarity and long range dependence, its characterization via the Hurst parameter H requires sophisticated techniques that often yield ambiguous results. In this work we show that fBm series map into a scale free visibility graph whose degree distribution is a function of H. Concretely, it is shown that the exponent of the power law degree distribution depends linearly on H. This also applies to fractional Gaussian noises (fGn) and generic f^(-b) noises. Taking advantage of these facts, we propose a brand new methodology to quantify long range dependence in these series. Its reliability is confirmed with extensive numerical simulations and analytical developments. Finally, we illustrate this method quantifying the persistent behavior of human gait dynamics.