Title: Bayesian nonparametric sparse VAR models
Authors: Monica Billio - University of Venice (Italy)
Roberto Casarin - University Ca' Foscari of Venice (Italy) [presenting]
Luca Rossini - Vrije Universiteit Amsterdam (Netherlands)
Abstract: In a high dimensional setting, vector autoregressive (VAR) models require a large number of parameters to be estimated and suffer from inferential problems. We propose a nonparametric Bayesian framework and introduce a new two-stage hierarchical Dirichlet process prior (DPP) for VAR models. This prior allows us to avoid overparametrization and overfitting issues by shrinking the coefficients toward a small number of random locations and induces a random partition of the coefficients, which is the main inference target of nonparametric Bayesian models. We use the posterior random partition to cluster coefficients into groups and to estimate the number of groups. Our nonparametric Bayesian model with multiple shrinkage prior is well suited for extracting Granger causality networks from time series, since it allows us to capture some common features of real-world networks, which are sparsity, blocks or communities structures, heterogeneity and clustering in the strength or intensity of the edges. In order to fully capture the richness of the data, it is therefore crucial that the model used to extract network accounts for weights associated to the edges. We illustrate the benefits of our approach by extracting network structures from panel data for shock transmission in business cycles and in financial markets.