Inference in Bayesian Additive Vector Autoregressive Tree Models

Vector autoregressive (VAR) models assume linearity between the endogenous variables and their lags. This linearity assumption might be overly restrictive and could have a deleterious impact on forecasting accuracy. As a solution, we propose combining VAR with Bayesian additive regression tree (BART) models. The resulting Bayesian additive vector autoregressive tree (BAVART) model is capable of capturing arbitrary non-linear relations between the endogenous variables and the covariates without much input from the researcher. Since controlling for heteroscedasticity is key for producing precise density forecasts, our model allows for stochastic volatility in the errors. Using synthetic and real data, we demonstrate the advantages of our methods. For Eurozone data, we show that our nonparametric approach improves upon commonly used forecasting models and that it produces impulse responses to an uncertainty shock that are consistent with established findings in the literature.