Conferences at Department of Economics, University of Toronto, RCEF 2012: Cities, Open Economies, and Public Policy

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Multivariate Stochastic Volatility

William James McCausland, Shirley Miller, Denis Pelletier

Last modified: 2012-07-12


We propose a new technique for the analysis of multivariate stochastic volatility models, based on efficient draws of volatility from its conditional posterior distribution. It applies to models with several kinds of cross-sectional dependence. Full VAR coefficient and covariance matrices give cross-sectional volatility dependence. Mean factor structure allows conditional correlations, given states, to vary in time. The conditional return distribution features Student’s t marginals, with asset-specific degrees of freedom, and copulas describing cross-sectional dependence. We draw volatility as a block in the time dimension and one-at-a-time in the cross-section. Following McCausland (2012), we use close approximations of the conditional posterior distributions of volatility blocks as Metropolis-Hastings proposal distributions. We illustrate using daily return data for ten currencies. We report results for univariate stochastic volatility models and two multivariate models. 

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