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Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations

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Author Info
Annastiina Silvennoinen (School of Economics and Finance, Queensland University of Technology)
Timo Teräsvirta (Department of Economic Statistics, Stokholm School of Economics)

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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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Publisher Info
Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 168.

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Length: 39
Date of creation: 01 Oct 2005
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Handle: RePEc:uts:rpaper:168

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Related research
Keywords: multivariate GARCH; constant conditional correlation; dynamic conditional correlation; return comovement; variable correlation GARCH model; volatility model evaluation;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
G1 - Financial Economics - - General Financial Markets

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References listed on IDEAS
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  3. BAUWENS, Luc & LAURENT, SŽbastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
    Other versions:
  4. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January. [Downloadable!] (restricted)
  5. King, Mervyn A & Wadhwani, Sushil, 1990. "Transmission of Volatility between Stock Markets," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(1), pages 5-33. [Downloadable!] (restricted)
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  6. 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. [Downloadable!]
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  7. R-P. Berben & W.J. Jansen, 2001. "Comovement in International Equity Markets: a Sectoral View," MEB Series (discontinued) 2001-11, Netherlands Central Bank, Monetary and Economic Policy Department. [Downloadable!]
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  8. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04. [Downloadable!] (restricted)
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  11. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
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  16. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
    Other versions:
  2. Feng, Yuanhua, 2006. "A local dynamic conditional correlation model," MPRA Paper 1592, University Library of Munich, Germany. [Downloadable!]
  3. 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. [Downloadable!]
    Other versions:
  4. Nektarios Aslanidis & Denise R. Osborn & Marianne Sensier, 2008. "Comovements between US and UK stock prices: the roles of macroeconomic information and timevarying conditional correlations," The School of Economics Discussion Paper Series 0805, Economics, The University of Manchester. [Downloadable!]
    Other versions:
  5. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Multivariate GARCH models," CREATES Research Papers 2008-06, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
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