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Universal window size-dependent transition of correlations in complex systems.

Tao Wu¹, Feng An², Xiangyun Gao¹

¹School of Economics and Management, China University of Geosciences, Beijing 100083, China.

Chaos (Woodbury, N.Y.)

|March 1, 2023

Summary

Choosing the right window size for time-varying correlation analysis is crucial. This study reveals a transition point from chaotic to nonchaotic states, offering a quantitative rule for optimal window selection in various systems.

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Area of Science:

Data Science
Complex Systems Analysis
Time Series Analysis

Background:

Pairwise correlations are vital for quantifying interactions in time series data.
Estimating correlations using sliding windows results in time-varying and window size-dependent measures.
Selecting an appropriate window size for correlation analysis remains a significant challenge.

Purpose of the Study:

To develop a framework for determining optimal window sizes in time-varying correlation analysis.
To investigate the relationship between window size and system state transitions (chaotic to nonchaotic).
To establish a quantitative rule for window size selection based on observed phenomena.

Main Methods:

Utilizing nonlinear correlation measurements within sliding windows to approximate time-varying correlations.
Analyzing the transition from chaotic-like to nonchaotic states as a function of increasing window size.
Validating the observed universal transition phenomenon across model and real-world systems.

Main Results:

A clear state transition from chaotic-like to nonchaotic dynamics was observed with increasing window size.
This window size-dependent transition was identified as a universal phenomenon in climate, financial, and neural systems.
The identified transition point offers a quantitative criterion for selecting optimal window sizes.

Conclusions:

The transition point from chaotic-like to nonchaotic correlation provides a robust method for window size selection.
Optimal window sizes, identified via this transition, enhance the accuracy of regression-based predictions.
The framework offers a universal approach applicable to diverse scientific and financial time series analysis.