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

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 timescales. The method employs q-dependent minimum spanning trees (qMSTs) to visualize evolving network structures. Using minute-by-minute exchange rate data for 140 cryptocurrencies on Binance (January 2021--October 2024), a rolling window analysis reveals significant shifts in qMSTs, notably around April 2022 during the Terra/Luna crash. Initially centralized around Bitcoin (BTC), the network later decentralized, with Ethereum 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 qMSTs 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 qMSTs' effectiveness in uncovering fluctuation-dependent correlations, with potential applications beyond finance, including biology, social and other complex systems.