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We proposed a data-driven approach to dissect multivariate time series inorder to discover multiple phases underlying dynamics of complex systems. Thiscomputing approach is developed as a multiple-dimension version of HierarchicalFactor Segmentation(HFS) technique. This expanded approach proposes asystematic protocol of choosing various extreme events in multi-dimensionalspace. Upon each chosen event, an empirical distribution of event-recurrence,or waiting time between the excursions, is fitted by a geometric distributionwith time-varying parameters. Iterative fittings are performed across allchosen events. We then collect and summarize the local recurrent patterns intoa global dynamic mechanism. Clustering is applied for partitioning the wholetime period into alternating segments, in which variables are identicallydistributed. Feature weighting techniques are also considered to compensate forsome drawbacks of clustering. Our simulation results show that this expandedapproach can even detect systematic differences when the joint distributionvaries. In real data experiments, we analyze the relationship from returns,trading volume, and transaction number of a single, as well as of multiplestocks in S&P500. We can successfully not only map out volatile periods butalso provide potential associative links between stocks.

Discovering Multiple Phases of Dynamics by Dissecting Multivariate Time Series