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 data 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 posteriors that can be drawn from a Gibbs
sampler. We compare the forecasting performance
of DAELasso to that of other popular Bayesian methods using US macro economic data.
The results suggest that DAELasso is a useful complement to the available Baysian
VAR shrinkage methods.