Flexible Bayesian MIDAS: Time-Variation, Group-Shrinkage and Sparsity

We propose a mixed-frequency regression prediction approach that models a time-varying trend and stochastic volatility in the trend and in the variable of interest.The coefficients of high-frequency indicators are regularized via a shrinkage prior that accounts for the grouping structure and within-group correlation among lags.A new sparsification algorithm on the posterior motivated by Bayesian decision theory derives inclusion probabilities over lag groups, thus making the results easy to communicate without imposing sparsity a priori.An empirical application on nowcasting UK GDP growth suggests that group-shrinkage improves nowcasting performance by relying on signals from a meaningful sub-set of predictors that include "hard" real activity indicators and, early in the data release, cycle additionally a number of surveys.Over the Covid-19 pandemic, a few additional indicators for the service and housing sectors are exploited that capture the disruptions from economic lockdowns.Accounting for a trend and stochastic volatility helps to stabilize the sparse nature of the variable selection during periods of large shocks, while accounting for uncertainty, especially early in the data release cycle.