Bayesian nonparametric sparse VAR models

TL;DR

This paper introduces a Bayesian nonparametric Lasso prior for high-dimensional VAR models, enhancing estimation and prediction by effectively clustering and shrinking coefficients, which aids in extracting meaningful causal networks from complex time series data.

Contribution

It proposes a novel BNP-Lasso prior that addresses overparametrization and overfitting in high-dimensional VAR models, capturing network structures with sparsity and heterogeneity.

Findings

Improved estimation efficiency and prediction accuracy.

Effective extraction of causal networks with realistic stylized facts.

Clustering and shrinking enhance interpretability of time series relationships.

Abstract

High dimensional vector autoregressive (VAR) models require a large number of parameters to be estimated and may suffer of inferential problems. We propose a new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional VAR models that can improve estimation efficiency and prediction accuracy. Our hierarchical prior overcomes overparametrization and overfitting issues by clustering the VAR coefficients into groups and by shrinking the coefficients of each group toward a common location. Clustering and shrinking effects induced by the BNP-Lasso prior are well suited for the extraction of causal networks from time series, since they account for some stylized facts in real-world networks, which are sparsity, communities structures and heterogeneity in the edges intensity. In order to fully capture the richness of the data and to achieve a better understanding of financial and macroeconomic risk, it is therefore crucial that the model used to extract network accounts for these stylized facts.