Bayesian Nonparametric Sparse Vector Autoregressive Models

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.