Bayesian modelling of VAR precision matrices using stochastic block networks

TL;DR

This paper introduces a novel Bayesian prior for VAR error precision matrices that incorporates shock network structures via stochastic block models, improving network recovery and forecast accuracy.

Contribution

It proposes a new prior on the VAR error precision matrix that models shock networks directly, enhancing structure learning and forecasting in VARs.

Findings

Accurately recovers true shock network structures in simulations.

Improves density forecast performance on US macroeconomic data.

Clusters shocks effectively based on network structure.

Abstract

Commonly used priors for Vector Autoregressions (VARs) induce shrinkage on the autoregressive coefficients. Introducing shrinkage on the error covariance matrix is sometimes done but, in the vast majority of cases, without considering the network structure of the shocks and by placing the prior on the lower Cholesky factor of the precision matrix. In this paper, we propose a prior on the VAR error precision matrix directly. Our prior, which resembles a standard spike and slab prior, models variable inclusion probabilities through a stochastic block model that clusters shocks into groups. Within groups, the probability of having relations across group members is higher (inducing less sparsity) whereas relations across groups imply a lower probability that members of each group are conditionally related. We show in simulations that our approach recovers the true network structure well. Using a US macroeconomic data set, we illustrate how our approach can be used to cluster shocks together and that this feature leads to improved density forecasts.