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Positivity Constraints on the Conditional Variances in the Family of Conditional Correlation GARCH Models

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  • Nakatani, Tomoaki

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    ()
    (CREATES, School of Economics and Management, University of Aarhus)

Abstract

In this article, we derive a set of necessary and sufficient conditions for positivity of the vector conditional variance equation in multivariate GARCH models with explicit modelling of conditional correlation. These models include the constant conditional correlation GARCH model of Bollerslev (1990) and its extensions. Under the new conditions, it is possible to introduce negative volatility spillovers in the model. An empirical example illustrates usefulness of having such conditions in practice.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 675.

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Length: 10 pages
Date of creation: 15 Oct 2007
Date of revision: 15 Nov 1007
Publication status: Published in Finance Research Letters, 2008, pages 88-95.
Handle: RePEc:hhs:hastef:0675

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Keywords: Multivariate GARCH; positivity constraints; conditional correlation;

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References

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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  2. Silvennoinen, Annastiina & Teräsvirta, Timo, 2005. "Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations," Working Paper Series in Economics and Finance, Stockholm School of Economics 577, Stockholm School of Economics, revised 01 Oct 2005.
  3. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 14(01), pages 70-86, February.
  4. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(3), pages 339-50, July.
  5. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(3), pages 351-62, July.
  6. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(01), pages 122-150, February.
  7. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 10(2), pages 229-35, April.
  8. Nakatani, Tomoaki & Teräsvirta, Timo, 2007. "Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model," Working Paper Series in Economics and Finance, Stockholm School of Economics 649, Stockholm School of Economics, revised 24 Jan 2007.
  9. He, Changli & Teräsvirta, Timo, 2002. "An application of the analogy between vector ARCH and vector random coefficient autoregressive models," Working Paper Series in Economics and Finance, Stockholm School of Economics 516, Stockholm School of Economics.
  10. Kawakatsu, Hiroyuki, 2006. "Matrix exponential GARCH," Journal of Econometrics, Elsevier, Elsevier, vol. 134(1), pages 95-128, September.
  11. Tsai, Henghsiu & Chan, Kung-Sik, 2008. "A Note On Inequality Constraints In The Garch Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(03), pages 823-828, June.
  12. C. Gourieroux, 2007. "Positivity Conditions for a Bivariate Autoregressive Volatility Specification," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(4), pages 624-636, Fall.
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Cited by:
  1. Christian Conrad & Menelaos Karanasos, 2008. "Modeling Volatility Spillovers between the Variabilities of US Inflation and Output: the UECCC GARCH Model," Working Papers, University of Heidelberg, Department of Economics 0475, University of Heidelberg, Department of Economics, revised Sep 2008.
  2. Carnero M. Angeles & Eratalay M. Hakan, 2014. "Estimating VAR-MGARCH models in multiple steps," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 18(3), pages 27, May.
  3. Le Pen, Yannick & Sévi, Benoît, 2009. "News and correlations: an impulse response analysis," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/6804, Paris Dauphine University.
  4. Conrad, Christian & Weber, Enzo, 2013. "Measuring Persistence in Volatility Spillovers," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79850, Verein für Socialpolitik / German Economic Association.
  5. Haas, Markus, 2010. "Covariance forecasts and long-run correlations in a Markov-switching model for dynamic correlations," Finance Research Letters, Elsevier, Elsevier, vol. 7(2), pages 86-97, June.
  6. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers, European University Institute ECO2012/19, European University Institute.

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