Bayesian dynamic variable selection in high dimensions

This paper proposes a variational Bayes algorithm for computationally efficient posterior and predictive inference in time-varying parameter (TVP) regression models. Within this context we specify a new dynamic variable/model selection strategy for TVP dynamic regression models in the presence of a large number of predictors. The proposed variational Bayes dynamic variable selection (VBDVS) algorithm allows for assessing at each time period in the sample which predictors are relevant (or not) for forecasting the dependent variable. The algorithm is applied to the problem of forecasting inflation using over 400 macroeconomic, financial and global predictors, many of which are potentially irrelevant or short-lived. We find that the new methodology is able to ensure parsimonious solutions to this high-dimensional estimation problem, that translate into excellent forecast performance.