Maximal spanning trees, asset graphs and random matrix denoising in the analysis of dynamics of financial networks

TL;DR

This paper compares the stability and cluster structure of financial networks derived from correlation matrices of stock returns, highlighting differences between ordinary and denoised matrices and their implications for understanding market dynamics.

Contribution

It introduces a detailed analysis of how denoising affects the stability and economic interpretability of correlation-based financial networks.

Findings

Ordinary correlation matrices are more stable over time than denoised ones.

Cluster structures are clearer in networks based on ordinary correlation matrices.

Denoising can obscure meaningful economic clusters.

Abstract

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.