Network structure of multivariate time series

TL;DR

This paper introduces a scalable, non-parametric multiplex network method for analyzing multivariate time series, enabling the detection of complex dynamical behaviors and financial crises without requiring phase space partitioning.

Contribution

The authors propose a novel multiplex network approach for multivariate time series analysis that is simple, general, and effective for large, heterogeneous, and non-stationary data.

Findings

Successfully detects transitions in coupled chaotic systems.

Identifies onset of synchronization phenomena.

Discriminates financial crises from stable periods.

Abstract

Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range of tools and techniques for time series analysis already exist, the increasing availability of massive data structures calls for new approaches for multidimensional signal processing. We present here a non-parametric method to analyse multivariate time series, based on the mapping of a multidimensional time series into a multilayer network, which allows to extract information on a high dimensional dynamical system through the analysis of the structure of the associated multiplex network. The method is simple to implement, general, scalable, does not require ad hoc phase space partitioning, and is thus suitable for the analysis of large, heterogeneous and non-stationary time series. We show that simple structural descriptors of the associated multiplex networks allow to extract and quantify nontrivial properties of coupled chaotic maps, including the transition between different dynamical phases and the onset of various types of synchronization. As a concrete example we then study financial time series, showing that a multiplex network analysis can efficiently discriminate crises from periods of financial stability, where standard methods based on time-series symbolization often fail.