The motifs of risk transmission in multivariate time series: Application to commodity prices

In this article we propose to exploit topological information embedded in forecast error variance decomposition derived from large Bayesian vector autoregressive models (VAR) to study network connectedness and risk transmission of multivariate time series observations. Firstly, we design a robust link classification procedure based on shortest paths, so to identify salient directional spillovers in a high-dimensional framework. Secondly, we study recurrent and statistically significant sub-graphs, i.e. network motifs, on the induced network backbone by means of null models which account for local node heterogeneity. The methodology is applied to analyze spillover networks of a set of global commodity prices. We demonstrate that spillovers become key drivers of the system variance during commodity price bubbles and bursts, giving raise to complex triadic structures which do not manifest during normal business periods. By accounting for local node connectivity, we observe a departure from the null models due to the high participation of Crude Oil, Food and Beverages and Raw Materials in complex recurrent sub-graphs.