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Multivariate stochastic volatility

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Author Info
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)

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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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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
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Handle: RePEc:tky:fseres:2007cf488

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  3. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November. [Downloadable!] (restricted)
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  4. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October. [Downloadable!] (restricted)
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  15. Adelchi Azzalini, 2005. "The Skew-normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 32(2), pages 159-188. [Downloadable!] (restricted)
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  19. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Oxford University Press for Biometrika Trust, vol. 89(3), pages 603-616, August.
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  21. Kawakatsu, Hiroyuki, 2006. "Matrix exponential GARCH," Journal of Econometrics, Elsevier, vol. 134(1), pages 95-128, September. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Alin Sima, 2008. "Stylized Facts and Discrete Stochastic Volatility Models," Advances in Economic and Financial Research - DOFIN Working Paper Series 10, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB. [Downloadable!]
  2. Gianni Amisano & Roberto Casarin, 2008. "Particle Filters for Markov-Switching Stochastic-Correlation Models," Working Papers 0814, University of Brescia, Department of Economics. [Downloadable!]
  3. Roberto Casarin & Domenico sartore, 2008. "Matrix-State Particle Filter for Wishart Stochastic Volatility Processes," Working Papers 0816, University of Brescia, Department of Economics. [Downloadable!]
  4. Roxana Chiriac & Valeri Voev, 2008. "Modelling and Forecasting Multivariate Realized Volatility," CoFE Discussion Paper 08-06, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
    Other versions:
  5. K. Triantafyllopoulos, 2008. "Multivariate stochastic volatility using state space models," Quantitative Finance Papers 0802.0223, arXiv.org. [Downloadable!]
  6. Gao, Jiti & McAleer, Michael & Allen, Dave, 2006. "Econometric modelling in finance and risk management: An overview," MPRA Paper 11978, University Library of Munich, Germany, revised Nov 2007. [Downloadable!]
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  7. Monica Billio & Massimiliano Caporin, 2006. "A generalized Dynamic Conditional Correlation Model for Portfolio Risk Evaluation," Working Papers 2006_53, University of Venice "Ca' Foscari", Department of Economics. [Downloadable!]
  8. K. Triantafyllopoulos, 2008. "Multivariate stochastic volatility with Bayesian dynamic linear models," Quantitative Finance Papers 0802.0214, arXiv.org. [Downloadable!]
  9. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Multivariate GARCH models," CREATES Research Papers 2008-06, School of Economics and Management, University of Aarhus. [Downloadable!]
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  10. Chia-Lin Chang & Michael McAleer & Roengchai Tansuchat, 2009. "Volatility Spillovers Between Crude Oil Futures Returns and Oil Company Stocks Return," CIRJE F-Series CIRJE-F-639, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  11. Casas, Isabel & Gao, Jiti, 2006. "Econometric estimation in long-range dependent volatility models: Theory and practice," MPRA Paper 11981, University Library of Munich, Germany, revised Aug 2007. [Downloadable!]
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  12. Michael McAleer & Marcelo Cunha Medeiros, 2006. "Realized volatility: a review," Textos para discussão 531 Publication status: F, Department of Economics PUC-Rio (Brazil). [Downloadable!]
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  13. Hafner, Christian M. & Manner, Hans, 2008. "Dynamic stochastic copula models: Estimation, inference and applications," Research Memoranda 043, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  14. Gregory H. Bauer & Keith Vorkink, 2007. "Multivariate Realized Stock Market Volatility
    ," Working Papers 07-20, Bank of Canada. [Downloadable!]
  15. Jun Yu & Renate Meyer, 2004. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Working Papers 23-2004, Singapore Management University, School of Economics. [Downloadable!]
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