Coupling between time series: a network view

TL;DR

This paper introduces the cross-visibility graph, a new method to analyze the coupling between two time series by mapping their relationship into a complex network, revealing correlation structures.

Contribution

The paper presents a novel cross-visibility algorithm and demonstrates its effectiveness in detecting coupling and correlation patterns in both synthetic and real-world time series data.

Findings

Correlated time series produce scale-free cross-visibility networks.

Uncorrelated series lead to non-power-law degree distributions.

Real-world financial data shows significant coupling detected by the method.

Abstract

Recently, the visibility graph has been introduced as a novel view for analyzing time series, which maps it to a complex network. In this paper, we introduce new algorithm of visibility, "cross-visibility", which reveals the conjugation of two coupled time series. The correspondence between the two time series is mapped to a network, "the cross-visibility graph", to demonstrate the correlation between them. We applied the algorithm to several correlated and uncorrelated time series, generated by the linear stationary ARFIMA process. The results demonstrate that the cross-visibility graph associated with correlated time series with power-law auto-correlation is scale-free. If the time series are uncorrelated, the degree distribution of their cross-visibility network deviates from power-law. For more clarifying the process, we applied the algorithm to real-world data from the financial trades of two companies, and observed significant small-scale coupling in their dynamics.