Bayesian MIDAS penalized regressions: Estimation, selection, and prediction

We propose a new approach to mixed-frequency regressions in high-dimensional environment that resorts Group Lasso penalization and Bayesian estimation inference. In particular, improve the prediction properties of model its sparse recovery ability, we consider with spike-and-slab prior. Penalty hyper-parameters governing shrinkage are automatically tuned via an adaptive MCMC algorithm. establish good frequentist asymptotic posterior error, recover optimal contraction rate, show optimality predictive density. Simulations proposed models have selection forecasting performance small samples, even when design matrix presents cross-correlation. When applied U.S. GDP, our penalized can outperform many strong competitors. Results suggest financial variables may some, although very limited, short-term content.