Statistically validated coeherence and intensity in temporal networks of information flows

We propose a method for characterizing the local structure of weighted multivariate time series networks. We draw intensity and coherence of network motifs, i.e. statistically recurrent subgraphs, to characterize the system behavior via higher-order structures derived upon effective transfer entropy networks. The latter consists of a model-free methodology enabling to correct for small sample biases affecting Shannon transfer entropy, other than conducting inference on the estimated directional time series information flows. We demonstrate the usefulness of our proposed method with an application to a set of global commodity prices. Our main result shows that, despite simple triadic structures are the most intense, coherent and statistically recurrent over time, their intensity suddenly decreases after the Global Financial Crisis, in favor of most complex triadic structures, while all types of subgraphs tend to become more coherent thereafter.