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When is a Copula Constant? A Test for Changing Relationships

  • Fabio Busetti
  • Andrew Harvey

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:, Oxford University Press.

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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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  1. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge.
  2. Kristin J. Forbes & Roberto Rigobon, 2002. "No Contagion, Only Interdependence: Measuring Stock Market Comovements," Journal of Finance, American Finance Association, vol. 57(5), pages 2223-2261, October.
  3. Sanjiv Ranjan Das & Raman Uppal, 2004. "Systemic Risk and International Portfolio Choice," Journal of Finance, American Finance Association, vol. 59(6), pages 2809-2834, December.
  4. de Jong, Robert M. & Amsler, Christine & Schmidt, Peter, 2007. "A robust version of the KPSS test based on indicators," Journal of Econometrics, Elsevier, vol. 137(2), pages 311-333, April.
  5. Neil Shephard & Jurgen Doornik & Siem Jan Koopman, 1998. "Statistical algorithms for models in state space using SsfPack 2.2," Economics Series Working Papers 1998-W06, University of Oxford, Department of Economics.
  6. Harvey, Andrew & Streibel, Mariane, 1998. "Testing for a slowly changing level with special reference to stochastic volatility," Journal of Econometrics, Elsevier, vol. 87(1), pages 167-189, August.
  7. DeRossi, G. & Harvey, A., 2007. "Quantiles, Expectiles and Splines," Cambridge Working Papers in Economics 0660, Faculty of Economics, University of Cambridge.
  8. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0657, Faculty of Economics, University of Cambridge.
  9. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  10. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "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?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  11. 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.
  12. Andrew Patton, 2004. "Modelling Asymmetric Exchange Rate Dependence," Working Papers wp04-04, Warwick Business School, Finance Group.
  13. Jukka Nyblom & Andrew Harvey, 2001. "Testing against smooth stochastic trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 415-429.
  14. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.
  15. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
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