Bayesian nonparametric sparse seemingly unrelated regression model (SUR)

Monica Billio, Roberto Casarin and Luca Rossini

No 2016:20, Working Papers from Department of Economics, University of Venice "Ca' Foscari"

Abstract: Seemingly unrelated regression (SUR) models are used in studying the interactions among economic variables of interest. In a high dimensional setting and when applied to large panel of time series, these models have a large number of parameters to be estimated and suffer from inferential problems. We propose a Bayesian nonparametric hierarchical model for multivariate time series in order to avoid the overparametrization and overfitting issues and to allow for shrinkage toward multiple prior means with unknown location, scale and shape parameters. We propose a two-stage hierarchical prior distribution. The first stage of the hierarchy consists in a lasso conditionally independent prior distribution of the Normal-Gamma family for the SUR coefficients. The second stage is given by a random mixture distribution for the Normal-Gamma hyperparameters, which allows for parameter parsimony through two components. The first one is a random Dirac point-mass distribution, which induces sparsity in the SUR coefficients; the second is a Dirichlet process prior, which allows for clustering of the SUR coefficients. We provide a Gibbs sampler for posterior approximations based on introduction of auxiliary variables. Some simulated examples show the efficiency of the proposed methods. We study the effectiveness of our model and inference approach with an application to macroeconomics.

Keywords: Bayesian nonparametrics; Large VAR; MCMC; Mixture model; Dirichlet Process; Graphical Representation (search for similar items in EconPapers)
JEL-codes: C11 C13 C14 C32 C51 E17 (search for similar items in EconPapers)
Pages: 46 pages
Date: 2016
New Economics Papers: this item is included in nep-mac and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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