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Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations

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  • Silvennoinen, Annastiina

    ()
    (School of Finance and Economics)

  • Teräsvirta, Timo

    ()
    (CREATES, Aarhus University)

Abstract

In this paper we propose a new multivariate GARCH model with time-varying conditional correlation structure. The approach adopted here is based on the decomposition of the covariances into correlations and standard deviations. The time-varying conditional correlations change smoothly between two extreme states of constant correlations according to an endogenous or exogenous transition variable. An LM test is derived to test the constancy of correlations and LM and Wald tests to test the hypothesis of partially constant correlations. Analytical expressions for the test statistics and the required derivatives are provided to make computations feasible. An empirical example based on daily return series of five frequently traded stocks in the Standard & Poor 500 stock index completes the paper. The model is estimated for the full five-dimensional system as well as several subsystems and the results discussed in detail.

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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 577.

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Length: 38 pages
Date of creation: 07 Jan 2005
Date of revision: 01 Oct 2005
Publication status: Forthcoming as Silvennoinen, Annastiina and Timo Teräsvirta, 'Modelling conditional correlations in asset returns: A smooth transition approach' in Econometric Reviews.
Handle: RePEc:hhs:hastef:0577

Note: Forthcoming under a new title: Modelling conditional correlations in asset returns: A smooth transition approavh
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Keywords: Multivariate GARCH; Constant conditional correlation; Dynamic conditional correlation; Return comovement; Volatility model evaluation;

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  1. Bera, Anil K. & Kim, Sangwhan, 2002. "Testing constancy of correlation and other specifications of the BGARCH model with an application to international equity returns," Journal of Empirical Finance, Elsevier, vol. 9(2), pages 171-195, March.
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  8. Lin, Wen-Ling & Engle, Robert F & Ito, Takatoshi, 1994. "Do Bulls and Bears Move across Borders? International Transmission of Stock Returns and Volatility," Review of Financial Studies, Society for Financial Studies, vol. 7(3), pages 507-38.
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  11. 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).
  12. Chesnay, F. & Jondeau, E., 2000. "Does Correlation between Stock Returns Really Increase during Turbulent Period?," Working papers 73, Banque de France.
  13. 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.
  14. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
  15. 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.
  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. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
  18. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
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