# The EAS approach for graphical selection consistency in vector autoregression models

## TL;DR

This paper introduces the EAS approach for Bayesian inference in high-dimensional VAR models, providing theoretical guarantees for graphical selection consistency and demonstrating its effectiveness through simulations.

## Contribution

It develops the EAS methodology for posterior inference in Bayesian VAR models and proves its graphical selection consistency in high-dimensional settings.

## Key findings

- Proves pairwise and strong graphical selection consistency for EAS in VAR(1) models.
- Demonstrates robustness of EAS to model misspecification.
- Shows effectiveness of EAS in high-dimensional simulations.

## Abstract

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.