Bootstrap validation of links of a minimum spanning tree

TL;DR

This paper introduces two bootstrap methods to validate links in minimum spanning trees derived from multivariate data, enhancing the robustness analysis of complex systems like stock market networks.

Contribution

It compares two bootstrap procedures for validating minimum spanning trees, providing insights into their combined use for analyzing complex hierarchical systems.

Findings

Both bootstrap methods yield partly distinct, informative results.

Parallel use of methods improves robustness validation.

Application to stock data demonstrates method effectiveness.

Abstract

We describe two different bootstrap methods applied to the detection of a minimum spanning tree obtained from a set of multivariate variables. We show that two different bootstrap procedures provide partly distinct information that can be highly informative about the investigated complex system. Our case study, based on the investigation of daily returns of a portfolio of stocks traded in the US equity markets, shows the degree of robustness and completeness of the information extracted with popular information filtering methods such as the minimum spanning tree and the planar maximally filtered graph. The first method performs a "row bootstrap" whereas the second method performs a "pair bootstrap". We show that the parallel use of the two methods is suggested especially for complex systems presenting both a nested hierarchical organization together with the presence of global feedback channels.