Finding metastable states in real-world time series with recurrence networks

TL;DR

This paper presents a self-adaptive recurrence network method for detecting metastable states in complex real-world time series, effectively handling noise and missing data.

Contribution

It introduces a novel approach to determine recurrence thresholds and identify metastable states using entropy-based embedding and soft partitioning.

Findings

Method robust against noise and missing data

Effective in identifying metastable states in complex series

Applicable to real-world time series analysis

Abstract

In the framework of time series analysis with recurrence networks, we introduce a self-adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real-world time series. As initial step, we introduce a way to set the embedding parameters used to reconstruct the state space from the time series. We set them as the ones giving the maximum Shannon entropy for the first simultaneous minima of recurrence rate and Shannon entropy. To identify metastable states, as well as the transitions between them, we use a soft partitioning algorithm for module finding which is specifically developed for the case in which a system shows metastability. We illustrate our method with two complex time series examples. Finally, we show the robustness of our method for identifying metastable states. Our results suggest that our method is robust for identifying metastable states in complex time series, even when introducing considerable levels of noise and missing data points.