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Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations

  • Silvennoinen, Annastiina


    (School of Finance and Economics)

  • Teräsvirta, Timo


    (CREATES, Aarhus University)

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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Paper provided by Stockholm School of Economics in its series SSE/EFI 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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  1. 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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  14. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
  15. 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.
  16. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
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  18. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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