Inference in Bayesian additive vector autoregressive tree models

Abstract

Vector autoregressive (VAR) models assume linearity between the endogenous variables and their lags. This 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 nonlinear 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. We apply our model to two datasets. The first application shows that the BAVART model yields highly competitive forecasts of the U.S. term structure of interest rates. In a second application we estimate our model using a moderately sized Eurozone dataset to investigate the dynamic effects of uncertainty on the economy.