复杂系统中相关动态的过幅度依赖:对加密货币市场的应用
Marcin Wątorek1, Marija Bezbradica2, Martin Crane2
1Dublin City University, Cracow University of Technology, Faculty of Computer Science and Mathematics, Kraków, Poland and Adapt Research Centre, School of Computing, Dublin, Ireland.
Physical review. E
|November 18, 2025
概括
这项研究引入了一种新方法来分析使用q-dependent metrics和q-minimum spanning trees (qMSTs) 的加密货币相关性. 它揭示了网络转变,比如重大崩后的去中心化,为投资组合构建提供了洞察力.
科学领域:
- 量化金融 量化金融
- 网络科学 网络科学
- 复杂系统分析 复杂系统分析
背景情况:
- 传统的相关度量通常无法捕捉复杂系统中的动态变化.
- 加密货币市场表现出由市场事件影响的复杂和不断变化的相关结构.
- 了解这些动态对于风险管理和投资组合优化至关重要.
研究的目的:
- 开发一种用于分析复杂系统中不断演变的相关性结构的一般方法.
- 将这种方法应用于加密货币市场,使用q-依赖度量和q-最小跨度树 (qMSTs).
- 可视化和量化网络结构的演变,并确定影响相关性的关键市场事件.
主要方法:
- 使用依赖于q的偏移交叉相关系数 ρ ((q,s) 来捕捉不同波动幅度和时间尺度之间的相关性.
- 采用q-依赖的最小跨度树 (qMSTs) 来可视化不断变化的网络结构.
- 在每分钟的加密货币汇率数据 (140个加密货币,2021年1月至2024年10月) 上进行滚动窗口分析.
主要成果:
- 观察到qMSTs的显著变化,特别是在Terra/Luna撞击 (2022年4月) 周围.
- 加密货币网络从围绕比特币 (BTC) 的集中发展到更分散的结构,以太坊和其他人获得了突出地位.
- 中等规模波动显示出比大规模波动更强的相关性,基于大规模波动的qMST更分散.
- 主要的市场中断放大了相关差异,导致崩时的结构完全分散.
结论:
- qMSTs有效地揭示了复杂系统中的依赖波动的相关性.
- 这些发现表明,理解这些不断变化的相关性可以导致更灵活的最佳投资组合构建.
- 该方法具有超出金融领域的潜在应用,包括生物学,社会科学和其他复杂系统.
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