The EAS approach for graphical selection consistency in vector autoregression models

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 in understanding 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, and there exist no generalized fiducial investigations of VAR models. In this direction, we construct methodology via the $\epsilon$-admissible subsets (EAS) approach for 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, and demonstrate empirically that it is an effective strategy in high-dimensional settings.