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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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  1. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.
  2. Andrew Patton, 2004. "Modelling Asymmetric Exchange Rate Dependence," Working Papers wp04-04, Warwick Business School, Finance Group.
  3. Koopman, S.J.M. & Shephard, N. & Doornik, J.A., 1998. "Statistical Algorithms for Models in State Space Using SsfPack 2.2," Discussion Paper 1998-141, Tilburg University, Center for Economic Research.
  4. Kristin Forbes & Roberto Rigobon, 1999. "No Contagion, Only Interdependence: Measuring Stock Market Co-movements," NBER Working Papers 7267, National Bureau of Economic Research, Inc.
  5. 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, vol. 54(1-3), pages 159-178.
  6. De Rossi, Giuliano & Harvey, Andrew, 2009. "Quantiles, expectiles and splines," Journal of Econometrics, Elsevier, vol. 152(2), pages 179-185, October.
  7. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, 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. Jukka Nyblom & Andrew Harvey, 2001. "Testing against smooth stochastic trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 415-429.
  10. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  11. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
  12. 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.
  13. 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.
  14. 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.
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Cited by:
  1. Krämer, Walter & van Kampen, Maarten, 2011. "A simple nonparametric test for structural change in joint tail probabilities," Economics Letters, Elsevier, vol. 110(3), pages 245-247, March.
  2. S Zhang & I Paya & D Peel, 2009. "Linkages between Shanghai and Hong Kong stock indices," Working Papers 599248, Lancaster University Management School, Economics Department.
  3. Harvey, Andrew, 2010. "Tracking a changing copula," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 485-500, June.
  4. Chollete, Loran & Pena, Victor de la & Lu, Ching-Chih, 2009. "International Diversification: A Copula Approach," UiS Working Papers in Economics and Finance 2009/27, University of Stavanger.
  5. Liu, Xiaochun, 2011. "Modeling the time-varying skewness via decomposition for out-of-sample forecast," MPRA Paper 41248, University Library of Munich, Germany.
  6. Fabio Busetti, 2012. "On detecting end-of-sample instabilities," Temi di discussione (Economic working papers) 881, Bank of Italy, Economic Research and International Relations Area.
  7. Chollete, Loran & Ning, Cathy, 2009. "The Dependence Structure of Macroeconomic Variables in the US," UiS Working Papers in Economics and Finance 2009/31, University of Stavanger.

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