A note on objective Bayes analysis for graphical vector autoregressive models

Vector Autoregressive (VAR) models are widely used to estimate and forecast multivariate time series. However, the large number of parameters of VAR models can lead to unstable inference and inaccurate forecasts, particularly with many variables. For this reason, restrictions supported by the data are usually required.We propose an objective Bayes approach based on graphical VAR models for learning contemporaneous dependencies as well as dynamic interactions among variables. We show that, if the covariance matrix at each time is Markov with respect to the same decomposable graph, then the likelihood of a graphical VAR can be factorized as an ordinary decomposable graphical model. Additionally, using a fractional Bayes factor approach, we are able to obtain the marginal likelihood in closed form and perform Bayes graphical model selection with limited computational burden.