[Paper Review] Detecting Network Instability via Multiscale Detrended Cross-Correlations and MST Topology

Jose De Leon Miranda, Marina Dolfin+2 more|arXiv (Cornell University)|Feb 10, 2026

Complex Systems and Time Series Analysis0 citations

TL;DR

The paper introduces Elastic DCCR, a multiscale network instability metric that combines DCCA with MST filtering to detect scale-dependent topological shifts in cross-correlation networks, applied to global equity indices.

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.

Motivation & Objective

• Motivate the need to characterize how correlation networks reorganize across different investment horizons.
• Propose a scale-aware framework that captures multiscale changes in network topology without assuming covariance stationarity.
• Develop a finite-difference elastic measure to quantify how average MST length responds to observation scale.
• Demonstrate that Elastic DCCR signals instability during financial stress and reveals structure hidden in single-scale analyses.
• Compare the multiscale network approach with Diebold et al.'s DCC-GARCH framework to highlight different perspectives on connectedness.

Proposed method

• Compute scale-dependent DCCA coefficients between standardized, GARCH-filtered returns.
• Transform DCCA coefficients into a correlation-based distance using d_DCCA^{ij}(s,t)=sqrt{2[1-ρ_DCCA^{ij}(s,t)]}.
• Construct a time- and scale-dependent network and filter it with the Minimum Spanning Tree (MST) to obtain the backbone.
• Define Elastic DCCR(t) as the finite-difference of log MST length across two scales: Elastic DCCR(t)=[log L(s_long,t)−log L(s_short,t)]/[log s_long−log s_short].
• Analyze the time evolution of L(s,t) and its scaling to detect departures from local power-law behavior and multiscale structural shifts.
• Compare real market data with synthetic independent GARCH(1,1) benchmarks to assess genuine multivariate structure versus univariate volatility.

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.

Experimental results

Research questions

• RQ1 Do cross-market correlations reorganize across different observation horizons in a multiscale fashion?
• RQ2 Can the average MST length across scales capture scale-dependent topology changes indicative of instability?
• RQ3 Does the Elastic DCCR effectively identify periods of financial stress not visible in single-scale analyses?
• RQ4 How does the multiscale network approach compare to VAR-based Diebold et al. connectedness measures in capturing systemic risk?

Key findings

• Elastic DCCR rises during episodes of financial stress, signaling increased short-term coordination and contracted correlation distances.
• The metric reveals scale-dependent reconfigurations in MST topology not visible in single-horizon analyses.
• Real market data show departures from local power-law scaling in log L(s,t) versus log s, unlike synthetic GARCH benchmarks.
• Anomalies in Elastic DCCR align with major global shocks, such as Greek capital controls, Brexit, Wuhan lockdown, and vaccine announcements.
• The approach does not require covariance stationarity and provides a topological, multiscale view of connectedness that complements Diebold–Yilmaz measures.

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).