Bayesian Doubly Adaptive Elastic-Net Lasso for VAR Shrinkage

We develop a novel Bayesian doubly adaptive elastic-net Lasso (DAELasso) approach for VAR shrinkage. DAELasso achieves variable selection and coefficients shrinkage in a data based manner. It constructively deals with the explanatory variables that tend to be highly collinear by encouraging grouping effect. In addition, it allows for different degree of shrinkages for different coefficients. Rewriting the multivariate Laplace distribution as a scale mixture, we establish closed-form conditional posteriors that can be drawn from a Gibbs sampler. Empirical analysis shows that forecast results produced by DAELasso and its variants are comparable to that of other popular Bayesian methods, which provides further evidence that the forecast performances of large and medium sized Bayesian VARs are relatively robust to prior choices, and in practice simple Minnesota types of priors can be more attractive relative to their complex and well designed alternatives.