Coupling between time series: A network view
Recently, the visibility graph has been introduced as a novel method for analyzing time series, which maps a time series to a complex network. In this paper we introduce a 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 have applied the algorithm to several correlated and uncorrelated time series, generated by the linear stationary ARFIMA process, in order to better understand the results of the cross-visibility of empirical series. The comparison between the degree distribution of coupled and uncoupled (shuffled) series' networks demonstrates the emergence of super nodes (extremely high-degree nodes) in the uncoupled ones. Furthermore, we have applied the algorithm to real-world data from the financial trades of two companies and oil, and observed significant small-scale coupling in their dynamics.