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

TL;DR

This paper addresses the problem of detecting scale-dependent structural instability in complex networks, focusing on financial markets. It introduces a multiscale framework that combines Detrended Cross-Correlation Analysis (DCCA) with Minimum Spanning Tree (MST) filtering to produce a multiscale network descriptor, and defines the Elastic Detrended Cross-Correlation Ratio (Elastic DCCR) as a finite-difference estimate of how the average MST length $L(s,t)$ changes with the observation scale $s$. The main contributions are the construction of a scale-aware, nonstationarity-robust metric and its demonstration on global equity indices, where Elastic DCCR spikes align with major shocks and reveal topology changes invisible to single-scale analyses; the approach also offers a practical link to existing connectedness measures while providing broader applicability to other multiscale systems. The findings suggest that Elastic DCCR can serve as an early-warning-like indicator of systemic transitions and can be extended to domains such as climate networks, neuronal systems, and engineered infrastructures, where interaction strength depends on scale.

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.

Figures (15)

• Figure 1: DCCA distances between the S&P 500 and other indices, computed across DCCA scales ranging from $s = 10$ to $120$ days using a rolling window of $w = 250$ trading days.
• Figure 2: Time evolution of the density of MST-filtered 1-month DCCA distances (left) and the corresponding dynamics of the first four moments (right).
• Figure 3: Time evolution of the density of MST-filtered 4-month DCCA distances (left) and the corresponding dynamics of the first four moments (right).
• Figure 6: First- and second-order coefficients ($\alpha(t)$, $\beta(t)$) and fit quality ($R^2$) for real (left) and synthetic (right) data.
• Figure 7: $z$--score screening of the Elastic DCCR (ratio 74/11); anomalies defined by $|Z_t|>2.5$.