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Testing for volatility interactions in the Constant Conditional Correlation GARCH model

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  • Tomoaki Nakatani
  • Timo Terasvirta

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 generalized autoregressive conditional heteroskedasticity (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. Copyright The Author(s). Journal compilation Royal Economic Society 2009

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Bibliographic Info

Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 12 (2009)
Issue (Month): 1 (03)
Pages: 147-163

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Handle: RePEc:ect:emjrnl:v:12:y:2009:i:1:p:147-163

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  1. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(3), pages 339-50, July.
  2. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper, Institute of Social and Economic Research, Osaka University 0549, Institute of Social and Economic Research, Osaka University.
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  6. 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.
  7. Cifarelli, Giulio & Paladino, Giovanna, 2005. "Volatility linkages across three major equity markets: A financial arbitrage approach," Journal of International Money and Finance, Elsevier, Elsevier, vol. 24(3), pages 413-439, April.
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  9. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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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," Hannover Economic Papers (HEP), Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät dp-476, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  2. Nakatani, Tomoaki & Teräsvirta, Timo, 2008. "Positivity constraints on the conditional variances in the family of conditional correlation GARCH models," Finance Research Letters, Elsevier, Elsevier, vol. 5(2), pages 88-95, June.
  3. Djamel Kirat & Ibrahim Ahamada, 2009. "The impact of the European Union Emission Trading Scheme on electricity generation sectors," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00378317, HAL.
  4. 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.
  5. Kirat, Djamel & Ahamada, Ibrahim, 2011. "The impact of the European Union emission trading scheme on the electricity-generation sector," Energy Economics, Elsevier, Elsevier, vol. 33(5), pages 995-1003, September.
  6. 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.
  7. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers, European University Institute ECO2012/19, European University Institute.
  8. repec:hal:journl:halshs-00384496 is not listed on IDEAS
  9. 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.
  10. Haas, Markus, 2010. "Covariance forecasts and long-run correlations in a Markov-switching model for dynamic correlations," Finance Research Letters, Elsevier, Elsevier, vol. 7(2), pages 86-97, June.
  11. Wasel Shadat & Chris Orme, 2011. "An investigation of parametric tests of CCC assumption," The School of Economics Discussion Paper Series, Economics, The University of Manchester 1109, Economics, The University of Manchester.
  12. Tomasz Wozniak, 2012. "Testing Causality Between Two Vectors in Multivariate GARCH Models," Economics Working Papers, European University Institute ECO2012/20, European University Institute.
  13. repec:hal:wpaper:hal-00378317 is not listed on IDEAS
  14. Le Pen, Yannick & Sévi, Benoît, 2009. "News and correlations: an impulse response analysis," Economics Papers from University Paris Dauphine 123456789/6804, Paris Dauphine University.

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