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

Paper: arXiv 2509.18820

Authors: Marcin Wątorek, Marija Bezbradica, Martin Crane, Jarosław Kwapień, Stanisław Drożdż

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts including q-dependent detrended cross-correlation coefficients, graph theory (MSTs), and spectral analysis, indicating high mathematical density. Empirically, it utilizes minute-by-minute data for 140 cryptocurrencies over nearly four years with rolling window analysis, demonstrating a rigorous and backtest-ready methodology.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Analyze evolving correlation structures<br>in complex systems using fluctuation amplitude"] --> B["Data Input<br>Minute-by-minute exchange rates<br>140 cryptocurrencies on Binance<br>Jan 2021 - Oct 2024"]
  
  B --> C["Methodology<br>$q$-dependent DCCA coefficient $\rho(q,s)$<br>Rolling Window Analysis"]
  
  C --> D["Computation<br>Construct $q$-dependent<br>Minimum Spanning Trees ($q$MSTs)"]
  
  D --> E["Analysis<br>Spectral Analysis<br>Distance Metrics<br>Network Topology"]
  
  E --> F["Key Findings<br>BTC dominance declining<br>Network decentralization<br>Medium fluctuations show stronger correlations<br>Crises amplify correlation differences"]
  
  F --> G["Outcomes<br>General methodology for complex systems<br>Flexible optimal portfolio construction<br>Applications in biology, social systems"]

Cited References (115)

1. More is different. Broken symmetry and the nature of the hierarchical structure of science. (1972)
2. Complexity: A guided tour (2009)
3. Mandelbrot’s cascades: a legendary destiny (2015) — link
4. Bitcoin, blockchain, and cryptoassets: A comprehensive introduction (2020)
5. Cryptocurrency market structure: connecting emotions and economics (2019) — link
6. Multifractal detrended fluctuation analysis of nonstationary time series (2002) — link
7. Wavelet versus detrended fluctuation analysis of multifractal structures (2006) — link
8. Multifractal detrended cross-correlation analysis for two nonstationary signals (2008) — link

3 of 115 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.