Dynamic Coupling Index-Based Network Reconstruction for Heterogeneous Time Series Systems

Abstract

Learning networks from heterogeneous multivariate time series is a recurring problem across neuroscience, social science, and economics. Existing edge estimators sit at two extremes. Nonparametric correlation measures such as Pearson correlation, Spearman rank correlation, and mutual information are cheap but capture only simple coupling on near-stationary signals. Fully parametric approaches such as vector autoregression and DCC–GARCH model richer dynamics but need long records and degrade on large panels. The common middle, with moderate data, heterogeneous signals, and quasi-linear coupling, is served by neither. This paper introduces the Dynamic Coupling Index (DCI), a windowed correlation metric that fills this middle. DCI normalizes each signal against its own estimated period before taking a windowed inner product of the residuals. It reduces to Pearson correlation, adds a single per-signal hyperparameter, matches Pearson’s computational cost, and has a closed-form null variance for significance testing. We validate DCI on three testbeds with external ground truth. On synthetic networks it recovers time-varying community structure where Pearson correlation and mutual information fail. On EEG it recovers occipital alpha synchronization during eyes-closed rest and ranks a default-mode-proxy region above the rest of cortex in more subjects than either baseline. On the FRED-MD macroeconomic panel evaluated against NBER recession dates it separates recessions from expansions more sharply than the Forbes–Rigobon adjustment, Spearman correlation, Pearson correlation, and DCC–GARCH. DCI improves on standard correlation estimators when signals differ in scale, periodicity, or volatility.