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Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model

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  • Nakatani, Tomoaki

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    ()
    (School of Management and Economics)

Abstract

In this paper we propose a Lagrange multiplier test for volatility interactions among markets or assets. The null hypothesis is the Constant Conditional Correlation GARCH model in which volatility of an asset is described only through lagged squared innovations and volatility of its own. The alternative hypothesis is an extension of that model in which volatility is modelled as a linear combination not only of its own lagged squared innovations and volatility but also of those in the other equations while keeping the conditional correlation structure constant. This configuration enables us to test for volatility transmissions among variables in the model. Monte Carlo experiments show that the proposed test has satisfactory finite sample properties. The size distortions become negligible when the sample size reaches 2500. The test is applied to pairs of foreign exchange returns and individual stock returns. Results indicate that there seem to be volatility interactions in the pairs considered, and that significant interaction effects typically result from the lagged squared innovations of the other variables.

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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 649.

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Length: 21 pages
Date of creation: 05 Jan 2007
Date of revision: 24 Jan 2007
Publication status: Published in Econometrics Journal, 2009, pages 147-163.
Handle: RePEc:hhs:hastef:0649

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Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
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Keywords: Multivariate GARCH; Volatility interactions; Lagrange multiplier test; Monte Carlo simulation; Conditional correlations;

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References

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  1. Hamao, Yasushi & Masulis, Ronald W & Ng, Victor, 1990. "Correlations in Price Changes and Volatility across International Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 3(2), pages 281-307.
  2. 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.
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  5. 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.
  6. 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.
  7. Stephen G. Cecchetti & Robert E. Cumby & Stephen Figlewski, 1986. "Estimation of the optimal futures hedge," Research Working Paper 86-10, Federal Reserve Bank of Kansas City.
  8. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  9. 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.
  10. 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.
  11. Eklund, Bruno & Teräsvirta, Timo, 2003. "Testing constancy of the error covariance matrix in vector models," Working Paper Series in Economics and Finance 549, Stockholm School of Economics, revised 18 Jan 2006.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
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Citations

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Cited by:
  1. Stahl, Gerhard & Wang, Shaohui & Wendt, Markus, 2011. "Validate Correlation of an ESG: Treasury Yields across," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Leibniz Universität Hannover dp-476, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  2. repec:hal:wpaper:hal-00378317 is not listed on IDEAS
  3. 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.
  4. Tomasz Wozniak, 2012. "Testing Causality Between Two Vectors in Multivariate GARCH Models," Economics Working Papers ECO2012/20, European University Institute.
  5. Francq, Christian & Zakoian, Jean-Michel, 2010. "QML estimation of a class of multivariate GARCH models without moment conditions on the observed process," MPRA Paper 20779, University Library of Munich, Germany.
  6. Le Pen, Yannick & Sévi, Benoît, 2009. "News and correlations: an impulse response analysis," Economics Papers from University Paris Dauphine 123456789/6804, Paris Dauphine University.
  7. Nakatani, Tomoaki & Teräsvirta, Timo, 2007. "Positivity Constraints on the Conditional Variances in the Family of Conditional Correlation GARCH Models," Working Paper Series in Economics and Finance 675, Stockholm School of Economics, revised 15 Nov 1007.
  8. repec:hal:journl:halshs-00384496 is not listed on IDEAS
  9. Conrad, Christian & Karanasos, Menelaos, 2010. "Negative Volatility Spillovers In The Unrestricted Eccc-Garch Model," Econometric Theory, Cambridge University Press, vol. 26(03), pages 838-862, June.
  10. Kirat, Djamel & Ahamada, Ibrahim, 2011. "The impact of the European Union emission trading scheme on the electricity-generation sector," Energy Economics, Elsevier, vol. 33(5), pages 995-1003, September.
  11. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers ECO2012/19, European University Institute.
  12. Paul Catani & Timo Teräsvirta & Meiqun Yin, 2014. "A Lagrange Multiplier Test for Testing the Adequacy of the Constant Conditional Correlation GARCH Model," CREATES Research Papers 2014-03, School of Economics and Management, University of Aarhus.

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