Vector autoregressive (VAR) models aim to capture linear temporal interdependencies among multiple time series. They have been widely used in macro and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which provided novel insights into the role of temporal dependence for regularized estimates of the model’s parameters. However, hardly anything is known regarding properties of the posterior distribution for such models.

In this talk, we consider a VAR model with two prior choices for the autoregressive coefficient matrix: a non-hierarchical matrix-normal prior and a hierarchical prior which corresponds to an arbitrary scale mixture of normals. We establish posterior consistency for both these priors under standard regularity assumptions, when the dimension p of the VAR model grows with the sample size n (but still remains smaller than n). In particular, this establishes posterior consistency under a variety of shrinkage priors, which introduces (group) sparsity in the columns of the model coefficient matrices.