# Bayesian MIDAS Penalized Regressions: Estimation, Selection, and Prediction

## TL;DR

This paper introduces a Bayesian Group Lasso approach with spike-and-slab priors for high-dimensional mixed-frequency regressions, enhancing prediction accuracy and variable selection, especially in economic forecasting contexts.

## Contribution

It develops a novel Bayesian penalized regression method with adaptive hyper-parameter tuning, establishing theoretical properties and demonstrating superior empirical performance.

## Key findings

- Good selection and forecasting in small samples
- Outperforms competitors in U.S. GDP forecasting
- Limited short-term predictive power of financial variables

## Abstract

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