Common Drifting Volatility in Large Bayesian Vars

71 Pages Posted: 4 Apr 2012

See all articles by Andrea Carriero

Andrea Carriero

Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research

Todd E. Clark

Federal Reserve Bank of Cleveland

Massimiliano Giuseppe Marcellino

Bocconi University - Department of Economics; Centre for Economic Policy Research (CEPR)

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Date Written: March 2012

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.

Keywords: Bayesian VARs, forecasting, prior specification, stochastic volatility

JEL Classification: C11, C13, C33, C53

Suggested Citation

Carriero, Andrea and Clark, Todd E. and Marcellino, Massimiliano, Common Drifting Volatility in Large Bayesian Vars (March 2012). CEPR Discussion Paper No. DP8894, Available at SSRN: https://ssrn.com/abstract=2034112

Andrea Carriero (Contact Author)

Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research ( email )

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Todd E. Clark

Federal Reserve Bank of Cleveland ( email )

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Massimiliano Marcellino

Bocconi University - Department of Economics ( email )

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Italy

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom