We compare homoskedastic and heteroskedastic mixed frequency (MF) vector autoregression and Bayesian additive regression tree (BART) models to assess their performance in predicting tail risk at short horizons. MF-BART is a nonlinear state space model, and we discuss approximation-based approaches to devise a computationally efficient estimation algorithm. The models are applied in an out-of-sample exercise for quarterly and monthly macroeconomic variables in Italy. The proposed econometric refinements yield improvements in predictive accuracy.