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When is a Copula Constant? A Test for Changing Relationships

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  • Fabio Busetti
  • Andrew Harvey

Abstract

A copula defines the probability that observations from two time series lie below given quantiles. It is proposed that stationarity tests constructed from indicator variables be used to test against the hypothesis that the copula is changing over time. Tests associated with different quantiles may point to changes in different parts of the copula. The tests are still effective when prefiltering is carried out to correct for persistent changes in volatility. However, a "median quadrant association test" that is robust to changing volatility provides a good overall test against a time-varying copula. An empirical illustration on financial contagion is provided. (JEL: C12, G32) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

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Bibliographic Info

Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 9 (2011)
Issue (Month): 1 (Winter)
Pages: 106-131

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Handle: RePEc:oup:jfinec:v:9:y:2011:i:1:p:106-131

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References

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  1. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0657, Faculty of Economics, University of Cambridge.
  2. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, 05.
  3. Sanjiv Ranjan Das & Raman Uppal, 2004. "Systemic Risk and International Portfolio Choice," Journal of Finance, American Finance Association, American Finance Association, vol. 59(6), pages 2809-2834, December.
  4. Koopman, S.J.M. & Shephard, N. & Doornik, J.A., 1998. "Statistical Algorithms for Models in State Space Using SsfPack 2.2," Discussion Paper, Tilburg University, Center for Economic Research 1998-141, Tilburg University, Center for Economic Research.
  5. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  6. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0649, Faculty of Economics, University of Cambridge.
  7. Harvey, Andrew & Streibel, Mariane, 1998. "Testing for a slowly changing level with special reference to stochastic volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 87(1), pages 167-189, August.
  8. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, Elsevier, vol. 14(3), pages 401-423, June.
  9. Jukka Nyblom & Andrew Harvey, 2001. "Testing against smooth stochastic trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 16(3), pages 415-429.
  10. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0839, Faculty of Economics, University of Cambridge.
  11. DeRossi, G. & Harvey, A., 2007. "Quantiles, Expectiles and Splines," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0702, Faculty of Economics, University of Cambridge.
  12. van den Goorbergh, Rob W.J. & Genest, Christian & Werker, Bas J.M., 2005. "Bivariate option pricing using dynamic copula models," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 101-114, August.
  13. Kristin Forbes & Roberto Rigobon, 1999. "No Contagion, Only Interdependence: Measuring Stock Market Co-movements," NBER Working Papers 7267, National Bureau of Economic Research, Inc.
  14. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, Elsevier, vol. 54(1-3), pages 159-178.
  15. de Jong, Robert M. & Amsler, Christine & Schmidt, Peter, 2007. "A robust version of the KPSS test based on indicators," Journal of Econometrics, Elsevier, Elsevier, vol. 137(2), pages 311-333, April.
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Citations

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Cited by:
  1. Chollete, Loran & Pena, Victor de la & Lu, Ching-Chih, 2009. "International Diversification: A Copula Approach," UiS Working Papers in Economics and Finance, University of Stavanger 2009/27, University of Stavanger.
  2. S Zhang & I Paya & D Peel, 2009. "Linkages between Shanghai and Hong Kong stock indices," Working Papers, Lancaster University Management School, Economics Department 599248, Lancaster University Management School, Economics Department.
  3. Krämer, Walter & van Kampen, Maarten, 2011. "A simple nonparametric test for structural change in joint tail probabilities," Economics Letters, Elsevier, Elsevier, vol. 110(3), pages 245-247, March.
  4. Liu, Xiaochun, 2011. "Modeling the time-varying skewness via decomposition for out-of-sample forecast," MPRA Paper 41248, University Library of Munich, Germany.
  5. Wang, Yi-Chiuan & Wu, Jyh-Lin & Lai, Yi-Hao, 2013. "A revisit to the dependence structure between the stock and foreign exchange markets: A dependence-switching copula approach," Journal of Banking & Finance, Elsevier, Elsevier, vol. 37(5), pages 1706-1719.
  6. Thanaset Chevapatrakul & Kai-Hong Tee, 2014. "The Effects of News Events on Market Contagion: Evidence from the 2007-2009 Financial Crisis," Discussion Papers, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM) 2014/08, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
  7. Chollete, Loran & Ning, Cathy, 2009. "The Dependence Structure of Macroeconomic Variables in the US," UiS Working Papers in Economics and Finance, University of Stavanger 2009/31, University of Stavanger.
  8. Wied, Dominik & Dehling, Herold & van Kampen, Maarten & Vogel, Daniel, 2014. "A fluctuation test for constant Spearman’s rho with nuisance-free limit distribution," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 76(C), pages 723-736.
  9. Harvey, Andrew, 2010. "Tracking a changing copula," Journal of Empirical Finance, Elsevier, Elsevier, vol. 17(3), pages 485-500, June.
  10. Fabio Busetti, 2012. "On detecting end-of-sample instabilities," Temi di discussione (Economic working papers), Bank of Italy, Economic Research and International Relations Area 881, Bank of Italy, Economic Research and International Relations Area.

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