Structural learning of contemporaneous dependencies in graphical VAR models

An objective Bayes approach based on graphical modeling is proposed to learn the contemporaneous dependencies among multiple time series within the framework of Vector Autoregressive (VAR) models. Assuming that, at any time, the covariance matrix is Markov with respect to the same decomposable graph, it is shown that the likelihood of a graphical VAR can be factorized as an ordinary (decomposable) graphical model. Additionally, using a fractional Bayes factor approach, the marginal likelihood is obtained in closed form, and an MCMC algorithm for Bayesian graphical model determination with limited computational burden is presented. The method is validated through a simulation study and applied to a real data set concerning active users of the Earthquake Network application for smartphones.