  As evidenced by various recent and significant papers within the frequentist
literature, along with numerous applications in macroeconomics, genomics, and
neuroscience, there continues to be substantial interest to understand the
theoretical estimation properties of high-dimensional vector autoregression
(VAR) models. To date, however, while Bayesian VAR (BVAR) models have been
developed and studied empirically (primarily in the econometrics literature)
there exist very few theoretical investigations of the repeated sampling
properties for BVAR models in the literature. In this direction, we construct
methodology via the $\varepsilon$-$admissible$ subsets (EAS) approach for
posterior-like inference based on a generalized fiducial distribution of
relative model probabilities over all sets of active/inactive components
(graphs) of the VAR transition matrix. We provide a mathematical proof of
$pairwise$ and $strong$ graphical selection consistency for the EAS approach
for stable VAR(1) models which is robust to model misspecification, and
demonstrate numerically that it is an effective strategy in high-dimensional
settings.
