Superhighways and roads of multivariate time series shock transmission: Application to cryptocurrency, carbon emission and energy prices

Inferring the heterogeneous connection pattern of a networked system of multivariate time series observations is a key issue. In finance, the topological structure of financial connectedness in a network of assets can be a central tool for risk measurement. Against this, we propose a topological framework for variance decomposition analysis of multivariate time series in time and frequency domains. We build on the network representation of time–frequency generalized forecast error variance decomposition (GFEVD), and design a method to partition its maximal spanning tree into two components: (a) superhighways, i.e. the infinite incipient percolation cluster, for which nodes with high centrality dominate; (b) roads, for which low centrality nodes dominate. We apply our method to study the topology of shock transmission networks across cryptocurrency, carbon emission and energy prices. Results show that the topologies of short and long run shock transmission networks are starkly different, and that superhighways and roads considerably vary over time. We further document increased spillovers across the markets in the aftermath of the COVID-19 outbreak, as well as the absence of strong direct linkages between cryptocurrency and carbon markets.