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

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.