Higher-order organization of multivariate time series

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Several methods have been proposed for the analysis of multivariate time series, yet most of them neglect the effect of non-pairwise interactions on the emerging dynamics. Here, we propose a framework to characterize the temporal evolution of higher-order dependencies within multivariate time series. Using network analysis and topology, we show that our framework robustly differentiates various spatiotemporal regimes of coupled chaotic maps. This includes chaotic dynamical phases and various types of synchronization. Hence, using the higher-order co-fluctuation patterns in simulated dynamical processes as a guide, we highlight and quantify signatures of higher-order patterns in data from brain functional activity, financial markets and epidemics. Overall, our approach sheds light on the higher-order organization of multivariate time series, allowing a better characterization of dynamical group dependencies inherent to real-world data.