抑止交叉相关性及其随机矩阵极限:来自加密货币市场的一个例子
Stanisław Drożdż1,2, Paweł Jarosz2, Jarosław Kwapień1
1Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152, 31-342 Kraków, Poland.
Entropy (Basel, Switzerland)
|December 24, 2025
概括
复杂系统分析得到了一种新方法的改进,该方法分析了依赖规模和波动的相关性. 这种多分位式的阻断交叉相关系数 (ρr) 揭示了加密货币的真正相互依赖性,使其与噪音区别开来.
科学领域:
- 复杂系统分析 复杂系统分析
- 金融市场的动态 金融市场的动态
- 时间序列分析时间序列分析
背景情况:
- 传统的协差方法在复杂系统中与非静止性,长记忆和重尾斗争.
- 这些局限性掩盖了真正的相关性,阻碍了对金融市场和其他动态系统的准确分析.
研究的目的:
- 开发一种新的方法来分析复杂系统中的相关性,克服传统方法的局限性.
- 调查分离相关矩阵的光谱属性及其与随机情况的偏差.
- 将这个框架应用于加密货币市场,以确定强大的集体模式和真正的相互依赖.
主要方法:
- 构建了依赖于尺度和波动的相关性矩阵,使用多分形的分离交叉相关系数 (ρr).
- 检查了这些矩阵的光谱特性,并将它们与合成高斯式和q-高斯式信号进行了比较.
- 将框架应用于一分钟的加密货币回报 (2021-2024) 以分析市场和部门组件.
主要成果:
- 阻断,重尾和波动顺序参数 (r) 创建了偏离随机情况的光谱,即使没有交叉相关性.
- 对140种加密货币的分析揭示了占主导地位的市场因素和部门组成部分.
- 过市场模式允许清晰地识别结构显著的异常值,将经验数据与随机分离的交叉相关性极限对齐.
结论:
- 这项研究为复杂系统中分离的交叉相关性提供了精细的光谱基线.
- 多分位式偏离交叉相关系数 (ρr) 是一个有前途的工具,用于区分真正的相互依赖与噪声.
- 这种方法增强了对非静态,重尾系统的分析,特别是在金融市场.
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