Fast and Accurate Variational Inference for Large Bayesian VARs with Stochastic Volatility

TL;DR

This paper introduces a global variational approximation method for the joint posterior of log-volatility in large Bayesian VARs, significantly improving accuracy over existing local methods.

Contribution

It presents a novel global variational approximation approach for stochastic volatility in large Bayesian VARs, outperforming local methods in accuracy.

Findings

Global approximation is over an order of magnitude more accurate.

Method effectively models stochastic volatility in large VARs.

Application to 96-variable VAR demonstrates practical utility.

Abstract

We propose a new variational approximation of the joint posterior distribution of the log-volatility in the context of large Bayesian VARs. In contrast to existing approaches that are based on local approximations, the new proposal provides a global approximation that takes into account the entire support of the joint distribution. In a Monte Carlo study we show that the new global approximation is over an order of magnitude more accurate than existing alternatives. We illustrate the proposed methodology with an application of a 96-variable VAR with stochastic volatility to measure global bank network connectedness.