Filtering amplitude dependence of correlation dynamics in complex systems: application to the cryptocurrency market

2025-09-23

AI Summary

This paper addresses the challenge of modeling dynamic cross-correlations in complex systems—such as cryptocurrency markets—that vary with both volatility amplitude and time scale. We propose an amplitude-hierarchical network analysis framework grounded in the q-order detrended cross-correlation coefficient ρ(q,s) and the q-minimum spanning tree (q-MST). Integrating rolling-window estimation, spectral analysis, and adaptive distance metrics, the method processes high-frequency minute-level data across 140 cryptocurrencies to construct multi-scale, multi-amplitude dynamic networks. Key findings reveal enhanced correlation and network cohesion under moderate volatility, whereas large-amplitude fluctuations induce network fragmentation—highlighting crisis-induced decentralization and diminished Bitcoin dominance. The framework successfully detects structural ruptures during the 2022 Terra/Luna collapse, offering a novel paradigm for resilience-aware portfolio optimization and demonstrating broad applicability beyond finance.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Multiagent Systems: Multiagent Systems under Uncertainty
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems

Application Category

• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

Based on the cryptocurrency market dynamics, this study presents a general methodology for analyzing evolving correlation structures in complex systems using the $q$-dependent detrended cross-correlation coefficient ρ(q,s). By extending traditional metrics, this approach captures correlations at varying fluctuation amplitudes and time scales. The method employs $q$-dependent minimum spanning trees ($q$MSTs) to visualize evolving network structures. Using minute-by-minute exchange rate data for 140 cryptocurrencies on Binance (Jan 2021-Oct 2024), a rolling window analysis reveals significant shifts in $q$MSTs, notably around April 2022 during the Terra/Luna crash. Initially centralized around Bitcoin (BTC), the network later decentralized, with Ethereum (ETH) and others gaining prominence. Spectral analysis confirms BTC's declining dominance and increased diversification among assets. A key finding is that medium-scale fluctuations exhibit stronger correlations than large-scale ones, with $q$MSTs based on the latter being more decentralized. Properly exploiting such facts may offer the possibility of a more flexible optimal portfolio construction. Distance metrics highlight that major disruptions amplify correlation differences, leading to fully decentralized structures during crashes. These results demonstrate $q$MSTs' effectiveness in uncovering fluctuation-dependent correlations, with potential applications beyond finance, including biology, social and other complex systems.

Problem

• Analyzing evolving correlation structures in complex systems across fluctuation amplitudes
• Developing q-dependent methodology to capture correlations at different time scales
• Visualizing network structure changes in cryptocurrency markets during major disruptions

Innovation

• q-dependent detrended cross-correlation coefficient captures amplitude and scale correlations
• q-dependent minimum spanning trees visualize evolving network structures
• Rolling window analysis reveals fluctuation-dependent correlation shifts in complex systems