Bayesian Bi-level Sparse Group Regressions for Macroeconomic Density Forecasting

We construct optimal macroeconomic density forecasts in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is designed for a general model which encompasses forecasting models featuring either many covariates, or unknown nonlinearities, or series sampled at different frequencies. By relying on the novel concept of bi-level sparsity in time-series econometrics, our density forecasts are based on a prior that induces sparsity both at the group level and within groups. We demonstrate the consistency of both the predictive density and the posterior distribution of the model parameter. For the posterior distribution, we show that it contracts at the minimax-optimal rate and, asymptotically, puts mass on a set that includes the support of the model. While predictors in the same group are usually characterized by strong covariation and common characteristics and patterns, our theory allows for correlation even between groups. Finite sample performance is illustrated through Monte Carlo experiments and a real-data nowcasting exercise of the US GDP growth rate.