https://doi.org/10.1140/epjs/s11734-022-00687-3
Regular Article
Recurrence flow measure of nonlinear dependence
1
Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, 14473, Potsdam, Germany
2
Institute of Geoscience, University of Potsdam, Karl-Liebknecht-Straße 32, 14476, Potsdam, Germany
Received:
13
June
2022
Accepted:
27
September
2022
Published online:
11
October
2022
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. 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.
The original online version of this article was revised: There were two incorrect symbols in chapter two of the article, which in both cases should have been a lower case phi. The surname of the second author of the first reference in the reference list was incorrect and should have been Oświęcimka.
A correction to this article is available online at https://doi.org/10.1140/epjs/s11734-022-00706-3.
Copyright comment corrected publication 2022
© The Author(s) 2022. corrected publication 2022
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