Abstract
Seemingly unrelated regression (SUR) models are useful in studying the interactions among economic variables. In a high dimensional setting, these models require a large number of parameters to be estimated and suffer of inferential problems. To avoid overparametrization issues, we propose a hierarchical Dirichlet process prior (DPP) for SUR models, which allows shrinkage of coefficients toward multiple locations. We propose a two-stage hierarchical prior distribution, where the first stage of the hierarchy consists in a lasso conditionally independent prior of the Normal-Gamma family for the coefficients. The second stage is given by a random mixture distribution, which allows for parameter parsimony through two components: the first is a random Dirac point-mass distribution, which induces sparsity in the coefficients; the second is a DPP, which allows for clustering of the coefficients.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Banbura, M., Giannone, D., Reichlin, L.: Large Bayesian vector autoregressions. J. Appl. Econ. 25(1), 71–92 (2010)
Billio, M., Casarin, R., Rossini, L.: Bayesian nonparametric sparse seemingly unrelated regression model (2017). https://arxiv.org/abs/1608.02740
Carriero, A., Clark, T.E., Marcellino, M.: Bayesian VARs: specification choices and forecast accurancy. J. Appl. Econ. 30(1), 46–73 (2015)
Hatjispyros, S.J., Nicoleris, T.N., Walker, S.G.: Dependent mixtures of Dirichlet processes. Comput. Stat. Data Anal. 55(6), 2011–2025 (2011)
Koop, G.: Forecasting with medium and large Bayesian VARs. J. Appl. Econ. 28(2), 177–203 (2013)
Miller, R.: Bayesian analysis of the two-parameter gamma distribution. Technometrics 22(1) (1980)
Park, T., Casella, G.: The Bayesian Lasso. J. Am. Stat. Assoc. 103(482), 681–686 (2008)
Scott, S.L., Varian, H.R.: Predicting the present with Bayesian structural time series. Int. J. Math. Model. Numer. Optim. 5(1–2), 4–23 (2013)
Stock, J.H., Watson, M.W.: Generalized shrinkage methods for forecasting using many predictors. J. Bus. Econ. Stat. 30(4), 481–493 (2012)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B 58(1), 267–288 (1996)
Zellner, A.: An efficient method of estimating seemingly unrelated regressions and tests of aggregation bias. J. Am. Stat. Assoc. 57(298), 500–509 (1962)
Zellner, A.: An Introduction to Bayesian Inference in Econometrics. Wiley, New York (1971)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Billio, M., Casarin, R., Rossini, L. (2018). Bayesian Nonparametric Sparse Vector Autoregressive Models. In: Corazza, M., Durbán, M., Grané, A., Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-89824-7_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-89824-7_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-89823-0
Online ISBN: 978-3-319-89824-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)