Multivariate Stochastic Volatility
We provide a detailed summary of the large and vibrant emerging literature that deals with the multivariate modeling of conditional volatility of financial time series within the framework of stochastic volatility. The developments and achievements in this area represent one of the great success stories of financial econometrics. Three broad classes of multivariate stochastic volatility models have emerged: one that is a direct extension of the univariate class of stochastic volatility model, another that is related to the factor models of multivariate analysis and a third that is based on the direct modeling of time-varying correlation matrices via matrix exponential transformations, Wishart processes and other means. We discuss each of the various model formulations, provide connections and differences and show how the models are estimated. Given the interest in this area, further significant developments can be expected, perhaps fostered by the overview and details delineated in this paper, especially in the fitting of high-dimensional models.
KeywordsMarkov Chain Monte Carlo Stochastic Volatility Markov Chain Monte Carlo Algorithm Stochastic Volatility Model Full Conditional Distribution
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- Asai, M. and McAleer, M. (2007): The structure of dynamic correlations in multivariate stochastic volatility models. Unpublished paper: Faculty of Economics, Soka University.Google Scholar
- Chib, S. (2001): Markov chain Monte Carlo methods: Computation and inference. In: Heckman, J. J. and Leamer, E. (Eds.): Handbook of Econometrics 5, 3569–3649. North-Holland, Amsterdam.Google Scholar
- Doornik, J. A. (2002): Object-Oriented Matrix Programming Using Ox (3rd ed.). Timber-lake Consultants Press, London. http://www.nuff.ox.ac.uk/Users/Doornik.
- Ferreira, J. T. A. S. and Steel, M. F. J. (2004): Bayesian multivariate regression analysis with a new class of skewed distributions. Statistics Research Report 419, University of Warwick.Google Scholar
- Ghysels, E., Harvey, A. C. and Renault, E. (1996): Stochastic volatility. In: G. S. M. Rao, C. R. (Ed.): Statistical Models in Finance (Handbook of Statistics), 119–191. North-Holland, Amsterdam.Google Scholar
- Gourieroux, C., Jasiak, J. and Sufana, R. (2004): The Wishart autoregressive process of multivariate stochastic volatility. Discussion paper: University of Toronto.Google Scholar
- Jacquier, E., Polson, N. G. and Rossi, P. E. (1999): Stochastic volatility: Univariate and multivariate extensions. CIRANO Working paper 99s–26, Montreal.Google Scholar
- Pitt, M. K. and Shephard, N. (1999): Time varying covariances: a factor stochastic volatility approach. In: Bernardo, J. M., Berger, J. O., Dawid, A. P. and Smith, A. F. M. (Eds.): Bayesian Statistics 6, 547–570. Oxford University Press, Oxford.Google Scholar
- Shephard, N. (2004): Stochastic Volatility: Selected Readings. Oxford University Press, Oxford.Google Scholar
- Tsay, R. S. (2005). Analysis of Financial Time Series: Financial Econometrics (2nd ed.). Wiley, New York.Google Scholar