Complex Network Approach to Fractional Time Series

TL;DR

This paper explores the use of horizontal visibility graphs to analyze fractional time series, revealing how network properties relate to the Hurst exponent and improving correlation detection methods.

Contribution

It introduces the horizontal visibility algorithm for fractional processes, demonstrating its effectiveness over the traditional visibility algorithm in studying correlation properties.

Findings

Degree distributions follow parabolic exponential forms with Hurst-dependent parameters.

Topological measures can predict the Hurst exponent, except for anti-persistent fractional Gaussian noises.

Using Spearman correlation improves the analysis of fractional Gaussian noises.

Abstract

In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacency matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.