Complex Network Approach to Fractional Time Series

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.

References in corpus (4)

• From time series to complex networks: the visibility graph
• Complex Network Approach for Recurrence Analysis of Time Series
• Fully Developed Turbulence in the view of Horizontal Visibility Graphs
• Contagion spreading on complex networks with local deterministic dynamics

Cited by in corpus (5)

• Complex network approaches to nonlinear time series analysis
• Visibility graph analysis of wall turbulence time-series
• Visibility network analysis of large-scale intermittency in convective surface layer turbulence
• Nonlinear Correlations in Multifractals: Visibility Graphs of Magnitude and Sign Series
• Records in Fractal Stochastic Processes