Large Bayesian VARs: A flexible Kronecker error covariance structure

We introduce a class of large Bayesian vector autoregressions (BVARs) that allows for non-Gaussian, heteroscedastic and serially dependent innovations. To make estimation computationally tractable, we exploit a certain Kronecker structure of the likelihood implied by this class of models. We propose a unified approach for estimating these models using Markov chain Monte Carlo (MCMC) methods. In an application that involves 20 macroeconomic variables, we find that these BVARs with more flexible covariance structures outperform the standard variant with independent, homoscedastic Gaussian innovations in both in-sample model-fit and out-of-sample forecast performance.