  We propose a Machine Learning approach for optimal macroeconomic forecasting
in a high-dimensional setting with covariates presenting a known group
structure. Our model encompasses forecasting settings with many series, mixed
frequencies, and unknown nonlinearities. We introduce in time-series
econometrics the concept of bi-level sparsity, i.e. sparsity holds at both the
group level and within groups, and we assume the true model satisfies this
assumption. We propose a prior that induces bi-level sparsity, and the
corresponding posterior distribution is demonstrated to contract at the
minimax-optimal rate, recover the model parameters, and have a support that
includes the support of the model asymptotically. Our theory allows for
correlation between groups, while predictors in the same group can be
characterized by strong covariation as well as common characteristics and
patterns. Finite sample performance is illustrated through comprehensive Monte
Carlo experiments and a real-data nowcasting exercise of the US GDP growth
rate.
