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Modelling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH Model

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Author Info
Annastiina Silvennoinen
Timo Teräsvirta () (School of Economics and Management, University of Aarhus, Denmark)

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Abstract

In this paper we propose a multivariate GARCH model with a time-varying conditional correlation structure. The new Double Smooth Transition Conditional Correlation GARCH model extends the Smooth Transition Conditional Correlation GARCH model of Silvennoinen and Ter¨asvirta (2005) by including another variable according to which the correlations change smoothly between states of constant correlations. A Lagrange multiplier test is derived to test the constancy of correlations against the DSTCC–GARCH model, and another one to test for another transition in the STCC–GARCH framework. In addition, other specification tests, with the aim of aiding the model building procedure, are considered. Analytical expressions for the test statistics and the required derivatives are provided. The model is applied to a selection of world stock indices, and it is found that time is an important factor affecting correlations between them.

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Publisher Info
Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-05.

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Length: 32
Date of creation: 28 Jan 2008
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Handle: RePEc:aah:create:2008-05

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Web page: http://www.econ.au.dk/afn/

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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
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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  1. 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.
  2. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473. [Downloadable!] (restricted)
    Other versions:
  3. Engle, Robert & Colacito, Riccardo, 2006. "Testing and Valuing Dynamic Correlations for Asset Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 238-253, April. [Downloadable!] (restricted)
  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  5. Annastiina Silvennoinen & Timo Teräsvirta, 2005. "Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations," Research Paper Series 168, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
  6. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December. [Downloadable!] (restricted)
    Other versions:
  7. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series 2001-15, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
  8. Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 537-572. [Downloadable!] (restricted)
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  9. Berben, Robert-Paul & Jansen, W. Jos, 2005. "Comovement in international equity markets: A sectoral view," Journal of International Money and Finance, Elsevier, vol. 24(5), pages 832-857, September. [Downloadable!] (restricted)
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  10. Meitz, Mika & Saikkonen, Pentti, 2004. "Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models," Working Paper Series in Economics and Finance 573, Stockholm School of Economics, revised 20 Apr 2007. [Downloadable!]
    Other versions:
  11. 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. [Downloadable!] (restricted)
  12. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January. [Downloadable!] (restricted)
  13. 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, Oxford University Press for Society for Financial Studies, vol. 7(3), pages 507-38. [Downloadable!] (restricted)
  14. Martens, Martin & Poon, Ser-Huang, 2001. "Returns synchronization and daily correlation dynamics between international stock markets," Journal of Banking & Finance, Elsevier, vol. 25(10), pages 1805-1827, October. [Downloadable!] (restricted)
  15. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109. [Downloadable!]
  16. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04. [Downloadable!] (restricted)
  17. 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.
  18. Tse, Y. K., 2000. "A test for constant correlations in a multivariate GARCH model," Journal of Econometrics, Elsevier, vol. 98(1), pages 107-127, September. [Downloadable!] (restricted)
  19. 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. [Downloadable!] (restricted)
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