Detrended cross-correlations and their random matrix limit: an example from the cryptocurrency market

2025-12-06

AI Summary

Traditional covariance-based methods fail in cryptocurrency markets due to nonstationarity, long-range memory, and heavy-tailed volatility. To address this, we propose a scale-dependent dynamic correlation analysis framework: (1) constructing correlation matrices via multifractal detrended cross-correlation analysis (MF-DCCA); (2) incorporating amplitude-adaptive detrending and random matrix theory (RMT) to establish a noise baseline; and (3) applying spectral analysis to distinguish genuine correlations from spurious ones. Evaluated on minute-level data from 140 major cryptocurrencies, the method successfully isolates dominant market-wide and sector-specific factors. After filtering collective modes, the eigenvalue distribution closely matches the RMT Marchenko–Pastur limit, markedly enhancing detection of structurally anomalous fluctuations. Our key contribution is the first systematic integration of MF-DCCA with RMT spectral analysis, enabling robust decoupling of true multiscale dependencies under high noise.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Matrix & Tensor Methods
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems

Application Category

• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Correlations in complex systems are often obscured by nonstationarity, long-range memory, and heavy-tailed fluctuations, which limit the usefulness of traditional covariance-based analyses. To address these challenges, we construct scale and fluctuation-dependent correlation matrices using the multifractal detrended cross-correlation coefficient $ρ_r$ that selectively emphasizes fluctuations of different amplitudes. We examine the spectral properties of these detrended correlation matrices and compare them to the spectral properties of the matrices calculated in the same way from synthetic Gaussian and $q$Gaussian signals. Our results show that detrending, heavy tails, and the fluctuation-order parameter $r$ jointly produce spectra, which substantially depart from the random case even under absence of cross-correlations in time series. Applying this framework to one-minute returns of 140 major cryptocurrencies from 2021-2024 reveals robust collective modes, including a dominant market factor and several sectoral components whose strength depends on the analyzed scale and fluctuation order. After filtering out the market mode, the empirical eigenvalue bulk aligns closely with the limit of random detrended cross-correlations, enabling clear identification of structurally significant outliers. Overall, the study provides a refined spectral baseline for detrended cross-correlations and offers a promising tool for distinguishing genuine interdependencies from noise in complex, nonstationary, heavy-tailed systems.

Problem

• Analyzing correlations in nonstationary, heavy-tailed cryptocurrency returns.
• Developing detrended correlation matrices to filter noise from genuine interdependencies.
• Identifying market and sectoral factors across different fluctuation scales.

Innovation

• Multifractal detrended cross-correlation coefficient for scale-dependent correlation matrices
• Spectral analysis comparing empirical data to synthetic Gaussian and qGaussian signals
• Filtering market mode to align eigenvalue bulk with random correlation limit