Community Detection in Large Vector Autoregressions

We introduce a class of vector autoregressive (VAR) models in which the time series are partitioned into unknown communities. Spillovers are stronger between series that belong to the same community than otherwise. A natural question that arises in this framework is how to detect the communities from data. To this end, we propose an algorithm that uses the eigenvectors of a function of the estimated autoregressive matrices to consistently recover the communities. The methodology is applied to study clustering in industrial production among a group of major economies. We also introduce a regularised VAR estimator motivated by the algorithm, which performs favourably relative to a number of alternatives in an out-of-sample forecasting exercise