Oliver M. Cliff, Annie G. Bryant, Joseph T. Lizier, Naotsugu Tsuchiya & Ben D. Fulcher 
Nature Computational Science (2023)

Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems, but these computational methods—from contemporaneous correlation coefficients to causal inference methods—define and formulate interactions differently, using distinct quantitative theories that remain largely disconnected. Here we introduce a large assembled library of 237 statistics of pairwise interactions, and assess their behavior on 1,053 multivariate time series from a wide range of real-world and model-generated systems. Our analysis highlights commonalities between disparate mathematical formulations of interactions, providing a unified picture of a rich interdisciplinary literature. Using three real-world case studies, we then show that simultaneously leveraging diverse methods can uncover those most suitable for addressing a given problem, facilitating interpretable understanding of the quantitative formulation of pairwise dependencies that drive successful performance. Our results and accompanying software enable comprehensive analysis of time-series interactions by drawing on decades of diverse methodological contributions.

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