Michel Lubrano: michel.lubrano[at]univ-amu.fr
Pierre Michel: pierre.michel[at]univ-amu.fr
In this paper we construct optimal forecasts for macroeconomic aggregates in presence of a large number of series that can be cast into groups. The aim is to provide policymakers with tools that accurately track economic conditions in real time. The variables in each group have strong covariation and common characteristics and patterns. The group structure is exploited by designing a convenient prior that induces a bi-level sparsity – at the group level and within group. Such a sparsity structure mirrors the fact that not all predictors are relevant to forecast the target series, conditional on the remaining groups and predictors. This is particularly true when there are many predictors weakly correlated with the target variable, as it is often the case with predictors arising from alternative sources. Under the assumption that the true data generating process exhibits this bi-level sparse structure, our posterior distribution is able to recover the optimal forecast asymptotically and its support is made of parameters with at most the same sparsity as the true sparse model. The rate of contraction of the posterior distribution is recovered. Finite sample properties of our procedure are illustrated through Monte Carlo experiments. We illustrate the performance of our procedure with real data through a nowcasting exercise of the quarterly growth rate of the US GDP.