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Detrended Cross-Correlations and Their Random Matrix Limit: An Example from the Cryptocurrency Market.

Stanisław Drożdż1,2, Paweł Jarosz2, Jarosław Kwapień1

  • 1Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152, 31-342 Kraków, Poland.

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|December 24, 2025
PubMed
Summary
This summary is machine-generated.

Complex systems analysis is improved by a new method analyzing scale- and fluctuation-dependent correlations. This multifractal detrended cross-correlation coefficient (ρr) reveals genuine interdependencies in cryptocurrencies, distinguishing them from noise.

Keywords:
cryptocurrency marketdetrended cross-correlation analysiseigenvalue spectramultifractal cross-correlationsrandom matrix theory

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Area of Science:

  • Complex Systems Analysis
  • Financial Market Dynamics
  • Time Series Analysis

Background:

  • Traditional covariance methods struggle with nonstationarity, long memory, and heavy tails in complex systems.
  • These limitations obscure genuine correlations, hindering accurate analysis of financial markets and other dynamic systems.

Purpose of the Study:

  • To develop a novel method for analyzing correlations in complex systems that overcomes limitations of traditional approaches.
  • To investigate the spectral properties of detrended correlation matrices and their deviation from random cases.
  • To apply this framework to cryptocurrency markets to identify robust collective modes and genuine interdependencies.

Main Methods:

  • Constructed scale- and fluctuation-dependent correlation matrices using the multifractal detrended cross-correlation coefficient (ρr).
  • Examined spectral properties of these matrices and compared them with synthetic Gaussian and q-Gaussian signals.
  • Applied the framework to one-minute cryptocurrency returns (2021-2024) to analyze market and sectoral components.

Main Results:

  • Detrending, heavy tails, and the fluctuation-order parameter (r) create spectra deviating from random cases, even without cross-correlations.
  • Analysis of 140 cryptocurrencies revealed a dominant market factor and sectoral components.
  • Filtering the market mode allowed clear identification of structurally significant outliers, aligning empirical data with random detrended cross-correlation limits.

Conclusions:

  • The study provides a refined spectral baseline for detrended cross-correlations in complex systems.
  • The multifractal detrended cross-correlation coefficient (ρr) is a promising tool for distinguishing true interdependencies from noise.
  • This method enhances the analysis of nonstationary, heavy-tailed systems, particularly in financial markets.