Detecting Network Instability via Multiscale Detrended Cross-Correlations and MST Topology

TL;DR

This paper presents a multiscale network instability measure using Detrended Cross-Correlation Analysis and MST filtering, revealing scale-dependent reconfigurations in financial networks during stress periods.

Contribution

It introduces the Elastic Detrended Cross-Correlation Ratio (Elastic DCCR), a novel metric capturing network deformation across scales without assuming covariance stationarity.

Findings

Elastic DCCR rises sharply during financial stress episodes

Reveals scale-dependent network reconfigurations not visible in single-scale analysis

Highlights differences between stressed and stable market regimes

Abstract

We introduce a multiscale measure of network instability based on the joint use of Detrended Cross-Correlation Analysis (DCCA) and Minimum Spanning Tree (MST) filtering. The proposed metric, the Elastic Detrended Cross-Correlation Ratio (Elastic DCCR), is defined as a finite-difference measure of the logarithmic sensitivity of the average MST length to the observation scale. It captures how the structure of cross-correlation networks deforms across different investment horizons. When applied to a network of global equity indices, the Elastic DCCR rises sharply during episodes of financial stress, reflecting increased short-term coordination among investors and a contraction of correlation distances. The measure reveals scale-dependent reconfigurations in network topology that are not visible in single-scale analyses, and highlights clear differences between stressed and stable market regimes. The approach does not assume covariance stationarity and relies only on scale-dependent detrended correlations; as a result, it is broadly applicable to other complex systems in which interaction strength varies with scale.