标题： 多尺度复杂系统的经验相关矩阵的特征值分布及其在金融数据中的应用 显示英文标题

标题： Eigenvalue Distribution of Empirical Correlation Matrices for Multiscale Complex Systems and Application to Financial Data

摘要： 我们引入一种方法，用于描述多维时间序列相关矩阵的特征值分布。 利用我们新开发的矩阵H理论，我们通过考虑一个作为分层结构的级联信息模型，类似于科莫戈罗夫湍流的统计理论，改进了对多变量金融数据中经验相关矩阵特征值谱的描述。 我们的方法扩展了Marchenko-Pastur分布，以考虑不同的特征尺度，捕捉更大的数据方差比例，并挑战了传统噪声驱动金融市场的观点。 我们推测，该方法的有效性源于金融市场复杂性的增加，这由新的特征尺度和计算交易的增长所反映。 这些发现不仅支持湍流市场假说作为噪声的来源，还为经验相关矩阵中的噪声减少提供了一个实用框架，增强了资产之间真实市场相关性的推断。 显示英文摘要

摘要： We introduce a method for describing eigenvalue distributions of correlation matrices from multidimensional time series. Using our newly developed matrix H theory, we improve the description of eigenvalue spectra for empirical correlation matrices in multivariate financial data by considering an informational cascade modeled as a hierarchical structure akin to the Kolmogorov statistical theory of turbulence. Our approach extends the Marchenko-Pastur distribution to account for distinct characteristic scales, capturing a larger fraction of data variance, and challenging the traditional view of noise-dressed financial markets. We conjecture that the effectiveness of our method stems from the increased complexity in financial markets, reflected by new characteristic scales and the growth of computational trading. These findings not only support the turbulent market hypothesis as a source of noise but also provide a practical framework for noise reduction in empirical correlation matrices, enhancing the inference of true market correlations between assets.