A large Bayesian VAR with a block‐specific shrinkage: A forecasting application for Italian industrial production

This paper proposes a Bayesian vector autoregression (BVAR) model with the Kalman filter to forecast the Italian industrial production index in a pseudo real‐time experiment. Minnesota priors are adopted as a general framework, but a different shrinkage pattern is imposed for both the VAR coefficients and the Kalman gain, depending on the informative contribution of each variable investigated at frequency level. Both a time‐varying and a constant selection for the shrinkage are proposed. Overall, the new BVAR models significantly improve the forecasting performance in comparison with the more traditional versions based on standard Minnesota priors with a single shrinkage, equal for all the variables, and selected on the basis of some optimal criteria. Very promising results come out in terms of density forecasting as well.