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Positivity constraints on the conditional variances in the family of conditional correlation GARCH models

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  • Nakatani, Tomoaki
  • Teräsvirta, Timo

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. Review of Economics and Statistics 72, 498-505] 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

Article provided by Elsevier in its journal Finance Research Letters.

Volume (Year): 5 (2008)
Issue (Month): 2 (June)
Pages: 88-95

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Handle: RePEc:eee:finlet:v:5:y:2008:i:2:p:88-95

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  1. 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.
  2. 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.
  3. 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.
  4. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  5. 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.
  6. Silvennoinen, Annastiina & Teräsvirta, Timo, 2005. "Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations," Working Paper Series in Economics and Finance 577, Stockholm School of Economics, revised 01 Oct 2005.
  7. 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 516, Stockholm School of Economics.
  8. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  9. Kawakatsu, Hiroyuki, 2006. "Matrix exponential GARCH," Journal of Econometrics, Elsevier, vol. 134(1), pages 95-128, September.
  10. 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, vol. 20(3), pages 351-62, July.
  11. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
  12. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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Cited by:
  1. Conrad, Christian & Weber, Enzo, 2013. "Measuring Persistence in Volatility Spillovers," Working Papers 0543, University of Heidelberg, Department of Economics.
  2. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers ECO2012/19, European University Institute.
  3. 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.
  4. Le Pen, Yannick & Sévi, Benoît, 2009. "News and correlations: an impulse response analysis," Economics Papers from University Paris Dauphine 123456789/6804, Paris Dauphine University.
  5. 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).
  6. Haas, Markus, 2010. "Covariance forecasts and long-run correlations in a Markov-switching model for dynamic correlations," Finance Research Letters, Elsevier, vol. 7(2), pages 86-97, June.

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