Detecting scale-dependent network reconfiguration via multiscale detrended cross-correlations and MST topology

We introduce a multiscale measure of network reconfiguration 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 exhibits sharp deviations during episodes of financial stress, reflecting abrupt reorganisations of the scale-dependent geometry of cross-market correlations; the sign of the deviation distinguishes episodes of increasing from decreasing multiscale coherence. The measure reveals scale-dependent reconfigurations in network topology that are not visible in single-scale analyses, and highlights clear differences between periods of elevated market stress and periods of relative calm. 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.