Recurrence flow measure of nonlinear dependence

TL;DR

This paper introduces a recurrence-based dependence measure that quantifies nonlinear relationships in multivariate time series by analyzing the predictability of their joint evolution through recurrence plots, capturing multiple time scales without requiring parameters.

Contribution

The paper presents a novel recurrence flow measure that detects nonlinear dependencies and lagged correlations in high-dimensional systems, aiding delay selection and state space reconstruction.

Findings

Effectively captures lagged nonlinear correlations.

Identifies non-uniform delays in time series.

No parameters needed for recurrence plot analysis.

Abstract

Couplings in complex real-world systems are often nonlinear and scale-dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a high-dimensional nonlinear system. We propose a recurrence based dependence measure that quantifies the relationship between multiple time series based on the predictability of their joint evolution. The statistical analysis of recurrence plots (RPs) is a powerful framework in nonlinear time series analysis that has proven to be effective in addressing many fundamental problems, e.g., regime shift detection and identification of couplings. The recurrence flow through an RP exploits artifacts in the formation of diagonal lines, a structure in RPs that reflects periods of predictable dynamics. By using time-delayed variables of a deterministic uni-/multivariate system, lagged dependencies with potentially many time scales can be captured by the recurrence flow measure. Given an RP, no parameters are required for its computation. We showcase the scope of the method for quantifying lagged nonlinear correlations and put a focus on the delay selection problem in time-delay embedding which is often used for attractor reconstruction. The recurrence flow measure of dependence helps to identify non-uniform delays and appears as a promising foundation for a recurrence based state space reconstruction algorithm.