Discovering Multiple Phases of Dynamics by Dissecting Multivariate Time Series

TL;DR

This paper introduces a multivariate extension of Hierarchical Factor Segmentation to identify multiple dynamic phases in complex systems, using a systematic protocol and clustering to analyze real-world financial data.

Contribution

It develops a new multi-dimensional segmentation approach based on geometric distribution fitting and clustering, enhancing the detection of dynamic phases in multivariate time series.

Findings

Successfully detects systematic distribution differences.

Maps volatile periods in financial data.

Identifies potential links between stocks.

Abstract

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