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Title: Common Drifting Volatility in Large Bayesian VARs

Author(s): Andrea Carriero, Todd Clark and Massimiliano Marcellino

Publication Date: March 2012

Keyword(s): Bayesian VARs, forecasting, prior specification and stochastic volatility

Programme Area(s): International Macroeconomics

Abstract: The estimation of large Vector Autoregressions with stochastic volatility using standard methods is computationally very demanding. In this paper we propose to model conditional volatilities as driven by a single common unobserved factor. This is justified by the observation that the pattern of estimated volatilities in empirical analyses is often very similar across variables. Using a combination of a standard natural conjugate prior for the VAR coefficients, and an independent prior on a common stochastic volatility factor, we derive the posterior densities for the parameters of the resulting BVAR with common stochastic volatility (BVAR-CSV). Under the chosen prior the conditional posterior of the VAR coefficients features a Kroneker structure that allows for fast estimation, even in a large system. Using US and UK data, we show that, compared to a model with constant volatilities, our proposed common volatility model significantly improves model fit and forecast accuracy. The gains are comparable to or as great as the gains achieved with a conventional stochastic volatility specification that allows independent volatility processes for each variable. But our common volatility specification greatly speeds computations.

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Bibliographic Reference

Carriero, A, Clark, T and Marcellino, M. 2012. 'Common Drifting Volatility in Large Bayesian VARs'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=8894