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.