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Common Drifting Volatility in Large Bayesian VARs

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  • Andrea CARRIERO
  • Todd E. CLARK
  • Massimiliano MARCELLINO

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 Info

Paper provided by European University Institute in its series Economics Working Papers with number ECO2012/08.

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Date of creation: 2012
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Handle: RePEc:eui:euiwps:eco2012/08

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

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Cited by:
  1. Gary Koop & Dimitris Korobilis, 2012. "Large time-varying parameter VARs," Working Papers 2012_04, Business School - Economics, University of Glasgow.
  2. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2012. "Real-time nowcasting with a Bayesian mixed frequency model with stochastic volatility," Working Paper 1227, Federal Reserve Bank of Cleveland.
  3. Todd E. Clark & Francesco Ravazzolo, 2012. "The macroeconomic forecasting performance of autoregressive models with alternative specifications of time-varying volatility," Working Paper 1218, Federal Reserve Bank of Cleveland.
  4. Christine Garnier & Elmar Mertens & Edward Nelson, 2013. "Trend inflation in advanced economies," Finance and Economics Discussion Series 2013-74, Board of Governors of the Federal Reserve System (U.S.).

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