Recurrence-based time series analysis by means of complex network methods

TL;DR

This paper reviews recent methods that analyze time series through complex network techniques, especially recurrence plots, highlighting their potential to reveal structural features of dynamical systems beyond traditional approaches.

Contribution

It provides a comprehensive overview of recurrence-based complex network methods for time series analysis, discussing their potentials and limitations with practical examples.

Findings

Network measures reveal structural features of dynamical systems.

Recurrence-based methods complement traditional time series analysis.

Illustrated with both theoretical and real-world data.

Abstract

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.