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March 2022 Inference in Bayesian additive vector autoregressive tree models
Florian Huber, Luca Rossini
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Ann. Appl. Stat. 16(1): 104-123 (March 2022). DOI: 10.1214/21-AOAS1488

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.

Funding Statement

Florian Huber gratefully acknowledges funding from the Austrian Science Fund (FWF): ZK 35.

Acknowledgments

We would like to thank two anonymous reviewers, an Associate Editor as well as the Handling Editor for numerous comments that greatly improved the paper.

Citation

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Florian Huber. Luca Rossini. "Inference in Bayesian additive vector autoregressive tree models." Ann. Appl. Stat. 16 (1) 104 - 123, March 2022. https://doi.org/10.1214/21-AOAS1488

Information

Received: 1 August 2020; Revised: 1 April 2021; Published: March 2022
First available in Project Euclid: 28 March 2022

Digital Object Identifier: 10.1214/21-AOAS1488

Keywords: BAVART , Bayesian additive regression trees , decision trees , Nonparametric regression , vector autoregressions

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.16 • No. 1 • March 2022
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