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Negative Volatility Spillovers In The Unrestricted Eccc-Garch Model

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  • Conrad, Christian
  • Karanasos, Menelaos

Abstract

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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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 26 (2010)
Issue (Month): 03 (June)
Pages: 838-862

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Handle: RePEc:cup:etheor:v:26:y:2010:i:03:p:838-862_99

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  1. 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.
  2. 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.
  3. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
  4. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Modelling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH Model," CREATES Research Papers 2008-05, School of Economics and Management, University of Aarhus.
  5. Conrad, Christian, 2010. "Non-negativity conditions for the hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 157(2), pages 441-457, August.
  6. 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.
  7. 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.
  8. 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.
  9. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
  10. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  11. 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.
  12. 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.
  13. 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.
  14. Nakatani, Tomoaki & Teräsvirta, Timo, 2007. "Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model," Working Paper Series in Economics and Finance 649, Stockholm School of Economics, revised 24 Jan 2007.
  15. Olivier Ledoit & Pedro Santa-Clara & Michael Wolf, 2003. "Flexible Multivariate GARCH Modeling with an Application to International Stock Markets," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 735-747, August.
  16. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. Bai, Jushan & Chen, Zhihong, 2008. "Testing multivariate distributions in GARCH models," Journal of Econometrics, Elsevier, vol. 143(1), pages 19-36, March.
  18. Massimiliano Caporin, 2007. "Variance (Non) Causality in Multivariate GARCH," Econometric Reviews, Taylor and Francis Journals, vol. 26(1), pages 1-24.
  19. 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.
  20. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  21. 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.
  22. Scherrer, Wolfgang & Ribarits, Eva, 2007. "On The Parametrization Of Multivariate Garch Models," Econometric Theory, Cambridge University Press, vol. 23(03), pages 464-484, June.
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Cited by:
  1. Conrad, Christian, 2010. "Non-negativity conditions for the hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 157(2), pages 441-457, August.
  2. Christian Conrad & Menelaos Karanasos & Ning Zeng, 2008. "Multivariate Fractionally Integrated APARCH Modeling of Stock Market Volatility: A multi-country study," Working Papers 0472, University of Heidelberg, Department of Economics, revised Jul 2008.
  3. Tomasz Wozniak, 2012. "Testing Causality Between Two Vectors in Multivariate GARCH Models," Department of Economics - Working Papers Series 1139, The University of Melbourne.
  4. Christian Conrad & Menelaos Karanasos, 2008. "Modeling Volatility Spillovers between the Variabilities of US Inflation and Output: the UECCC GARCH Model," Working Papers 0475, University of Heidelberg, Department of Economics, revised Sep 2008.
  5. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers ECO2012/19, European University Institute.
  6. Conrad, Christian & Karanasos, Menelaos & Zeng, Ning, 2010. "The link between macroeconomic performance and variability in the UK," Economics Letters, Elsevier, vol. 106(3), pages 154-157, March.
  7. Nektarios Aslanidis & Isabel Casas, 2010. "Modelling asset correlations during the recent FInancial crisis: A semiparametric approach," CREATES Research Papers 2010-71, School of Economics and Management, University of Aarhus.
  8. M. Angeles Carnero Fernández & M. Hakan Eratalay, 2012. "Estimating VAR-MGARCH models in multiple steps," Working Papers. Serie AD 2012-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

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