Pruning a Minimum Spanning Tree

TL;DR

This paper introduces methods to filter noise from minimum spanning trees derived from stock market correlation matrices, enhancing the detection of meaningful connections during financial crises.

Contribution

It proposes two novel techniques—thresholding based on random network analysis and survival rate assessment—to improve the quality of minimum spanning trees in financial data.

Findings

Noise filtering improves network clarity during crises

Longer-lasting connections are more likely to be genuine

Combined techniques yield more robust financial networks

Abstract

This work employs some techniques in order to filter random noise from the information provided by minimum spanning trees obtained from the correlation matrices of international stock market indices prior to and during times of crisis. The first technique establishes a threshold above which connections are considered affected by noise, based on the study of random networks with the same probability density distribution of the original data. The second technique is to judge the strengh of a connection by its survival rate, which is the amount of time a connection between two stock market indices endure. The idea is that true connections will survive for longer periods of time, and that random connections will not. That information is then combined with the information obtained from the first technique in order to create a smaller network, where most of the connections are either strong or enduring in time.