Point and density forecasts for the euro area using Bayesian VARs

We evaluate variants of the Bayesian vector autoregressive (BVAR) model with respect to their relative and absolute forecast accuracies using point and density forecasts for euro area HICP inflation and GDP growth. We consider BVAR averaging with equal and optimal weights, Bayesian factor augmented VARs (BFAVARs), and large BVARs with ad-hoc, optimal, and estimated hyperparameters. BVAR averaging delivers relatively high RMSEs, but performs better in terms of predictive likelihoods. Large BVARs show the opposite pattern, while BFAVARs perform satisfactorily under both criteria. Continuous ranked probability scores indicate that large BVARs suffer most from extreme observations. Using calibration tests, we detect that most BVARs produce reasonable density forecasts for HICP inflation, but not for GDP growth. In an extensive sensitivity analysis, we show that large BVARs are an excellent choice for certain specifications (recursive estimation, 22 variables, iterative approach, and optimal or estimated hyperparameters), while BFAVARs are competitive under most specifications, and specifically when the cross section is large.