Modeling dynamic systems with linear parametric models usually suffer limitation which affects forecasting performance and policy implications. This paper advances a non-parametric autoregressive distributed lag model that employs a Bayesian additive regression tree (BART). The performance of the BART model is compared with selection models like Lasso, Elastic Net, and Bayesian networks in simulation experiments with linear and non-linear data generating processes (DGP), and on US macroeconomic time series data. The results show that the BART model is quite competitive against the linear parametric methods when the DGP is linear, and outperforms the competing methods when the DGP is non-linear. The empirical results suggest that the BART estimators are generally more efficient than the traditional linear methods when modeling and forecasting macroeconomic time series.
References
[1]
Chipman, H.A., George, E.I. and McCulloch, R.E. (2010) Bart: Bayesian Additive Regression Trees. The Annals of Applied Statistics, 4, 266-298. https://doi.org/10.1214/09-AOAS285
[2]
Hill, J.L. (2011) Bayesian Nonparametric Modeling for Causal Inference. Journal of Computational and Graphical Statistics, 20, 217-240. https://doi.org/10.1198/jcgs.2010.08162
[3]
Zeldow, B.M. (2017) Bayesian Nonparametric Methods for Causal Inference and Prediction. Doctor’s Thesis, University of Pennsylvania.
[4]
Sparapani, R., Logan, B.R., McCulloch, R.E. and Laud, P.W. (2020) Nonparametric Competing Risks Analysis Using Bayesian Additive Regression Trees. Statistical Methods in Medical Research, 29, 57-77. https://doi.org/10.1177/0962280218822140
[5]
Spanbauer, C. and Pan, W. (2022) Flexible Instrumental Variable Models with Bayesian Additive Regression Trees. arXiv: 2210.01872.
[6]
Zhang, J.L. and Härdle, W.K. (2010) The Bayesian Additive Classification Tree Applied to Credit Risk Modelling. Computational Statistics & Data Analysis, 54, 1197-1205. https://doi.org/10.1016/j.csda.2009.11.022
[7]
de Brito, D.A. and Artes, R. (2018) Application of Bayesian Additive Regression Trees in the Development of Credit Scoring Models in Brazil. Production, 28, e20170110. https://doi.org/10.1590/0103-6513.20170110
[8]
Clark, T.E., Huber, F., Koop, G., Marcellino, M. and Pfarrhofer, M. (2023) Tail Forecasting with Multivariate Bayesian Additive Regression Trees. International Economic Review, 64, 979-1022. https://doi.org/10.1111/iere.12619
[9]
Mumtaz, H. and Piffer, M. (2022) Impulse Response Estimation via Flexible Local Projections. arXiv: 2204.13150. https://doi.org/10.2139/ssrn.4088760
[10]
Jordà, Ò. (2005) Estimation and Inference of Impulse Responses by Local Projections. American Economic Review, 95, 161-182. https://doi.org/10.1257/0002828053828518
Huber, F. and Rossini, L. (2022) Inference in Bayesian Additive Vector Autoregressive Tree Models. The Annals of Applied Statistics, 16, 104-123. https://doi.org/10.1214/21-AOAS1488
[13]
Linero, A.R. and Antonelli, J.L. (2022) The How and Why of Bayesian Nonparametric Causal Inference. WIREs Computational Statistics,15, e1583. https://doi.org/10.1002/wics.1583
[14]
Wang, M., He, J. and Hahn, P.R. (2022) Local Gaussian Process Extrapolation for Bart Models with Applications to Causal Inference. Journal of Computational and Graphical Statistics. https://doi.org/10.1080/10618600.2023.2240384
[15]
Tibshirani, R. (1996) Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58, 267-288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x
[16]
Zou, H. and Hastie, T. (2005) Regularization and Variable Selection via the Elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67, 301-320. https://doi.org/10.1111/j.1467-9868.2005.00503.x
[17]
Hoerl, A.E. and Kennard, R.W. (1970) Ridge Regression: Applications to Nonorthogonal Problems. Technometrics, 12, 69-82. https://doi.org/10.1080/00401706.1970.10488635
[18]
Friedman, J., Hastie, T. and Tibshirani, R. (2010) Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, 33, 1-22. https://doi.org/10.18637/jss.v033.i01
[19]
Friedman, J.H. (1991) Multivariate Adaptive Regression Splines. The Annals of Statistics, 19, 1-67. https://doi.org/10.1214/aos/1176347963
[20]
Ahelegbey, D.F., Billio, M. and Casarin, R. (2016) Bayesian Graphical Models for Structural Vector Autoregressive Processes. Journal of Applied Econometrics, 31, 357-386. https://doi.org/10.1002/jae.2443
