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

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.

💡 Research Summary

The paper proposes a novel multiscale indicator of network instability called the Elastic Detrended Cross‑Correlation Ratio (Elastic DCCR). The authors combine Detrended Cross‑Correlation Analysis (DCCA), which can capture scale‑dependent long‑range correlations in non‑stationary time series, with Minimum Spanning Tree (MST) filtering, which extracts the backbone of a fully connected correlation network while discarding noisy cycles.

First, daily closing prices of nine major equity indices (the G7 plus China and Russia) from March 2013 to May 2023 are transformed into logarithmic returns. Each return series is filtered through a GARCH(1,1) model to remove heteroskedasticity, and the standardized residuals are used as inputs for DCCA. For a set of observation scales (s) ranging from 10 to 120 trading days, the DCCA coefficient (\rho_{ij}^{\text{DCCA}}(s)) is computed for every pair of indices. These coefficients are mapped to a distance metric (d_{ij}^{\text{DCCA}}(s)=\sqrt{2\bigl(1-\rho_{ij}^{\text{DCCA}}(s)\bigr)}) following the Mantegna construction, yielding a symmetric distance matrix for each scale.

Using Kruskal’s algorithm, an MST is built from the distance matrix at each scale and each rolling window (250‑day window, shifted by one day). The average edge length of the MST, \