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Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates

  • Andrew Patton
  • Yanqin Fan
  • Xiaohong Chen

Evidence that asset returns are more highly correlated during volatile markets and during market downturns (see Longin and Solnik, 2001, and Ang and Chen, 2002) has lead some researchers to propose alternative models of dependence. In this paper we develop two simple goodness-of-fit tests for such models. We use these tests to determine whether the multivariate Normal or the Student’s t copula models are compatible with U.S. equity return and exchange rate data. Both tests are robust to specifications of marginal distributions, and are based on the multivariate probability integral transform and kernel density estimation. The first test is consistent but requires the estimation of a multivariate density function and is recommended for testing the dependence structure between a small number of assets. The second test may not be consistent against all alternatives but it requires kernel estimation of only a univariate density function, and hence is useful for testing the dependence structure between a large number of assets. We justify our tests for both observable multivariate strictly stationary time series and for standardized innovations of GARCH models. A simulation study demonstrates the efficacy of both tests. When applied to equity return data and exchange rate return data, we find strong evidence against the normal copula, but little evidence against the more flexible Student’s t copula.

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Paper provided by Warwick Business School, Finance Group in its series Working Papers with number wp04-19.

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Date of creation: 2004
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Handle: RePEc:wbs:wpaper:wp04-19
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  1. Jean-David Fermanian, 2003. "Goodness of Fit Tests for Copulas," Working Papers 2003-34, Centre de Recherche en Economie et Statistique.
  2. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
  3. Frederick C. Mills, 1927. "Appendix to "The Behavior of Prices"," NBER Chapters, in: The Behavior of Prices, pages 441-586 National Bureau of Economic Research, Inc.
  4. Y. Malevergne & D. Sornette, 2001. "Testing the Gaussian Copula Hypothesis for Financial Assets Dependences," Papers cond-mat/0111310,
  5. Frederick C. Mills, 1927. "The Behavior of Prices," NBER Books, National Bureau of Economic Research, Inc, number mill27-1, December.
  6. Yanqin Fan & Paul Rilstone, 2001. "A Consistent Test for the Parametric Specification of the Hazard Function," Annals of Economics and Finance, Society for AEF, vol. 2(1), pages 77-96, May.
  7. Frederick C. Mills, 1927. "Introduction to "The Behavior of Prices"," NBER Chapters, in: The Behavior of Prices, pages 31-36 National Bureau of Economic Research, Inc.
  8. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
  9. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
  10. 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.
  11. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
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