标题： 随机相关矩阵谱性质的精细结构：对金融市场的一个应用 显示英文标题

标题： The fine structure of spectral properties for random correlation matrices: an application to financial markets

摘要： 我们研究金融相关矩阵特征值谱的一些性质。 特别是，我们探讨了在经验上观察到的大特征值块的性质，这些特征值块通常被认为是由金融数据中包含大量噪声所导致的。 我们通过一种过滤程序对两个数据集的经验相关矩阵进行处理，该程序突出了它们所包含的一些聚类结构，并分析这种过滤对特征值谱的影响。 我们表明，经验上观察到的特征值块是更小结构的叠加，而这些更小结构本身是股票之间交叉相关性的结果。 我们根据因子模型来解释和验证这些发现，并将经验谱与这类模型的随机矩阵理论预测谱进行比较。 显示英文摘要

摘要： We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross-correlations between stocks. We interpret and corroborate these findings in terms of factor models, and and we compare empirical spectra to those predicted by Random Matrix Theory for such models.