Inference in Bayesian Additive Vector Autoregressive Tree Models
This work addresses forecasting accuracy issues in econometrics by enabling non-linear modeling with minimal researcher input, though it is incremental as it combines existing VAR and BART methods.
The authors tackled the restrictive linearity assumption in vector autoregressive (VAR) models by proposing a Bayesian additive vector autoregressive tree (BAVART) model that captures arbitrary non-linear relations and includes stochastic volatility for precise density forecasts. They applied it to US interest rates, yielding highly competitive forecasts, and to a Eurozone dataset to investigate uncertainty effects on the economy.
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 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. We apply our model to two datasets. The first application shows that the BAVART model yields highly competitive forecasts of the US 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.