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Bayesian nonparametric sparse VAR models

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  • Monica Billio
  • Roberto Casarin
  • Luca Rossini

Abstract

In a high dimensional setting, vector autoregressive (VAR) models require a large number of parameters to be estimated and suffer of 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 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. Empirical evidences show that our methodology identifies the most relevant linkages between panel units and clustering effects in the linkages intensity. Also we find that the centrality of the nodes changes across intensity levels.

Suggested Citation

  • Monica Billio & Roberto Casarin & Luca Rossini, 2016. "Bayesian nonparametric sparse VAR models," Papers 1608.02740, arXiv.org, revised May 2018.
  • Handle: RePEc:arx:papers:1608.02740
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    References listed on IDEAS

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