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

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Abstract
We introduce a multiscale measure of network instability based on the joint use ofDetrended 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 duringepisodes of financial stress, reflecting increased short-term coordination amonginvestors and a contraction of correlation distances. The measure reveals scale-dependent reconfigurations in network topology thatare not visible in single-scale analyses, and highlights clear differencesbetween 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.

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