Forecasting Euro Area Macroeconomic Variables with Bayesian Adaptive Elastic Net

Abstract

I use the adaptive elastic net in a Bayesian framework and test its forecasting performance against lasso, adaptive lasso and elastic net (all used in a Bayesian framework) in a series of simulations, as well as in an empirical exercise for macroeconomic Euro area data. The results suggest that elastic net is the best model among the four Bayesian methods considered. Adaptive lasso, on the other hand, shows the worst forecasting performance. Lasso is generally better then adaptive lasso, but worse than adaptive elastic net. The differences in the performance of these models become especially large when the number of regressors grows considerably relative to the number of available observations. The results point to the fact that the ridge regression component in the elastic net is responsible for its improvement in forecasting performance over lasso. The adaptive shrinkage in some of the models does not seem to play a major role, and may even lead to a deterioration of the performance.