  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. Despite a plethora of methods have
been proposed for the analysis of multivariate time series, most of them
neglect the effect of non-pairwise interactions on the emerging dynamics. Here,
we propose a novel framework to characterize the temporal evolution of
higher-order dependencies within multivariate time series. Using network
analysis and topology, we show that, unlike traditional tools based on pairwise
statistics, our framework robustly differentiates various spatiotemporal
regimes of coupled chaotic maps, including 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 new light on the
higher-order organization of multivariate time series, allowing a better
characterization of dynamical group dependencies inherent to real-world data.
