Detecting groups in large vector autoregressions

This work introduces the stochastic block vector autoregressive (SB-VAR) model. In this class of vector autoregressions, the time series are partitioned into latent groups such that spillover effects are stronger among series that belong to the same group than otherwise. A key question that arises in this framework is how to detect the latent groups from a sample of observations generated by the model. To this end, we propose a group detection algorithm based on the eigenvectors of a function of the estimated autoregressive matrices. We establish that the proposed algorithm consistently detects the groups when the cross-sectional and time-series dimensions are sufficiently large. The methodology is applied to study the group structure of a panel of risk measures of top financial institutions in the United States and a panel of word counts extracted from Twitter.