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Multivariate stochastic volatility

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  • Siddhartha Chib

    (Olin School of Business, Washington Unviersity in St.Louis)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

  • Manabu Asai

    (Faculty of Economics, Soka University)

Abstract

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.

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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-488.

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Length: 39 pages
Date of creation: May 2007
Date of revision:
Handle: RePEc:tky:fseres:2007cf488

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