Variational Inference for Large Bayesian Vector Autoregressions

Abstract

We propose a novel variational Bayes approach to estimate high-dimensional Vector Autoregressive (VAR) models with hierarchical shrinkage priors. Our approach does not rely on a conventional structural representation of the parameter space for posterior inference. Instead, we elicit hierarchical shrinkage priors directly on the matrix of regression coefficients so that (a) the prior structure maps into posterior inference on the reduced-form transition matrix and (b) posterior estimates are more robust to variables permutation. An extensive simulation study provides evidence that our approach compares favorably against existing linear and nonlinear Markov chain Monte Carlo and variational Bayes methods. We investigate the statistical and economic value of the forecasts from our variational inference approach for a mean-variance investor allocating her wealth to different industry portfolios. The results show that more accurate estimates translate into substantial out-of-sample gains across hierarchical shrinkage priors and model dimensions.