Wu T, An F, Gao X, Liu S, Sun X, Wang Z, Su Z, Kurths J. Universal window size-dependent transition of correlations in complex systems.
CHAOS (WOODBURY, N.Y.) 2023;
33:023111. [PMID:
36859190 DOI:
10.1063/5.0134944]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Accepted: 01/23/2023] [Indexed: 06/18/2023]
Abstract
Correlation analysis serves as an easy-to-implement estimation approach for the quantification of the interaction or connectivity between different units. Often, pairwise correlations estimated by sliding windows are time-varying (on different window segments) and window size-dependent (on different window sizes). Still, how to choose an appropriate window size remains unclear. This paper offers a framework for studying this fundamental question by observing a critical transition from a chaotic-like state to a nonchaotic state. Specifically, given two time series and a fixed window size, we create a correlation-based series based on nonlinear correlation measurement and sliding windows as an approximation of the time-varying correlations between the original time series. We find that the varying correlations yield a state transition from a chaotic-like state to a nonchaotic state with increasing window size. This window size-dependent transition is analyzed as a universal phenomenon in both model and real-world systems (e.g., climate, financial, and neural systems). More importantly, the transition point provides a quantitative rule for the selection of window sizes. That is, the nonchaotic correlation better allows for many regression-based predictions.
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