Livan Giacomo, Alfarano Simone, Scalas Enrico
Dipartimento di Fisica Nucleare e Teorica, Università degli Studi di Pavia, Pavia, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jul;84(1 Pt 2):016113. doi: 10.1103/PhysRevE.84.016113. Epub 2011 Jul 29.
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 we compare empirical spectra to those predicted by random matrix theory for such models.
我们研究了金融相关矩阵特征值谱的一些性质。具体而言，我们调查了通过实证观察到的大特征值簇的性质，这些大特征值簇通常被认为是金融数据中所含大量噪声的结果。我们通过对两个数据集的实证相关矩阵应用一种突出其所含某些聚类结构的滤波程序来挑战这一常识，并分析这种滤波对特征值谱的影响。我们表明，通过实证观察到的特征值簇是较小结构的叠加，而这些较小结构又是股票之间交叉相关性的结果。我们根据因子模型对这些发现进行解释和佐证，并将实证谱与随机矩阵理论针对此类模型预测的谱进行比较。
