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Negative Volatility Spillovers in the Unrestricted ECCC-GARCH Model

This paper considers a formulation of the extended constant or time-varying conditional correlation GARCH model which allows for volatility feedback of either sign, i.e., positive or negative. In the previous literature, negative volatility spillovers were ruled out by the assumption that all the coefficients of the model are non- negative, which is a su±cient condition for ensuring the positive definiteness of the conditional covariance matrix. In order to allow for negative feedback, we show that the positive definiteness of the conditional covariance matrix can be guaranteed even if some of the parameters are negative. Thus, we extend the results of Nelson and Cao (1992) and Tsai and Chan (2008) to a multivariate setting. For the bivariate case of order one we look into the consequences of adopting these less severe restrictions and find that the flexibility of the process is substantially increased. Our results are helpful for the model-builder, who can consider the unrestricted formulation as a tool for testing various economic theories.

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Paper provided by KOF Swiss Economic Institute, ETH Zurich in its series KOF Working papers with number 08-189.

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Length: 27 pages
Date of creation: Feb 2008
Date of revision:
Handle: RePEc:kof:wpskof:08-189
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  1. Henghsiu Tsai & K. S. Chan, 2007. "A Note on Non-Negative Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 350-360, 05.
  2. Annastiina Silvennoinen & Timo Teräsvirta, 2009. "Modeling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH Model," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(4), pages 373-411, Fall.
  3. Bai, Jushan & Chen, Zhihong, 2008. "Testing multivariate distributions in GARCH models," Journal of Econometrics, Elsevier, vol. 143(1), pages 19-36, March.
  4. Conrad, Christian, 2010. "Non-negativity conditions for the hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 157(2), pages 441-457, August.
  5. Ledoit, Olivier & Santa-Clara, Pedro & Wolf, Michael, 1999. "Flexible Multivariate GARCH Modeling With an Application to International Stock Markets," University of California at Los Angeles, Anderson Graduate School of Management qt93s6p8gb, Anderson Graduate School of Management, UCLA.
  6. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Multivariate GARCH models," CREATES Research Papers 2008-06, School of Economics and Management, University of Aarhus.
  7. Massimiliano Caporin, 2007. "Variance (Non) Causality in Multivariate GARCH," Econometric Reviews, Taylor & Francis Journals, vol. 26(1), pages 1-24.
  8. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
  9. Stephen G. Cecchetti & Robert E. Cumby & Stephen Figlewski, 1986. "Estimation of the optimal futures hedge," Research Working Paper 86-10, Federal Reserve Bank of Kansas City.
  10. Christian M. Hafner, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 26-54.
  11. Scherrer, Wolfgang & Ribarits, Eva, 2007. "On The Parametrization Of Multivariate Garch Models," Econometric Theory, Cambridge University Press, vol. 23(03), pages 464-484, June.
  12. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
  13. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  14. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-35, April.
  15. Stilianos Fountas & Menelaos Karanasos & Jinki Kim, 2006. "Inflation Uncertainty, Output Growth Uncertainty and Macroeconomic Performance," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(3), pages 319-343, 06.
  16. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  17. Christian Conrad & Berthold R. Haag, 2006. "Inequality Constraints in the Fractionally Integrated GARCH Model," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(3), pages 413-449.
  18. Tsai, Henghsiu & Chan, Kung-Sik, 2008. "A Note On Inequality Constraints In The Garch Model," Econometric Theory, Cambridge University Press, vol. 24(03), pages 823-828, June.
  19. Karanasos, Menelaos, 1999. "The second moment and the autocovariance function of the squared errors of the GARCH model," Journal of Econometrics, Elsevier, vol. 90(1), pages 63-76, May.
  20. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
  21. Tomoaki Nakatani & Timo Terasvirta, 2009. "Testing for volatility interactions in the Constant Conditional Correlation GARCH model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 147-163, 03.
  22. 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.
  23. Logue, Dennis E & Sweeney, Richard James, 1981. "Inflation and Real Growth: Some Empirical Results: A Note," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 13(4), pages 497-501, November.
  24. He, Changli & Ter svirta, Timo, 2004. "An Extended Constant Conditional Correlation Garch Model And Its Fourth-Moment Structure," Econometric Theory, Cambridge University Press, vol. 20(05), pages 904-926, October.
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