金融网络动力学分析中的最大生成树、资产图和随机矩阵去噪
Maximal spanning trees, asset graphs and random matrix denoising in the analysis of dynamics of financial networks
摘要：
基于股票收益率的相关矩阵，研究了最大生成树和资产图的时间依赖性。在这些网络中，节点代表公司，链接与它们之间的相关系数有关。特别强调的是普通和去噪相关矩阵之间的比较。相应的网络的单步和多步生存率的分析表明，普通的相关矩阵是更稳定的时间比去噪的。我们的研究还表明，在去噪过程中，一些关于公司集群结构的信息丢失了。从经济角度来看，集群结构是有意义的，并且可以很容易地在基于去噪相关矩阵的网络中观察到。然而，这种结构在基于普通相关矩阵的网络中更加清晰。文中还介绍了随机矩阵去噪方法等技术方面的内容。
英文摘要：
We study the time dependence of maximal spanning trees and asset graphs based on correlation matrices of stock returns. In these networks the nodes represent companies and links are related to the correlation coefficients between them. Special emphasis is given to the comparison between ordinary and denoised correlation matrices. The analysis of single- and multi-step survival ratios of the corresponding networks reveals that the ordinary correlation matrices are more stable in time than the denoised ones. Our study also shows that some information about the cluster structure of the companies is lost in the denoising procedure. Cluster structure that makes sense from an economic point of view exists, and can easily be observed in networks based on denoised correlation matrices. However, this structure is somewhat clearer in the networks based on ordinary correlation matrices. Some technical aspects, such as the random matrix denoising procedure, are also presented.
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