We compare homoskedastic and heteroskedastic mixed frequency (MF) vector autoregression and Bayesian additive regression tree (BART) models to assess their relative performance in predicting tail risk.

MF-BART is a nonlinear state space model, and we discuss linear approximation approaches to devise computationally efficient estimation algorithms.

The models are applied in an out-of-sample backcasting, nowcasting and forecasting exercise for a set of quarterly and monthly macroeconomic variables in Italy. The proposed econometric refinements yield improvements in predictive accuracy.