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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

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  • Andrew Patton
  • Yanqin Fan
  • Xiaohong Chen

Abstract

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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Bibliographic Info

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. 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.
  2. Jean-David Fermanian, 2003. "Goodness of Fit Tests for Copulas," Working Papers 2003-34, Centre de Recherche en Economie et Statistique.
  3. Frederick C. Mills, 1927. "The Behavior of Prices," NBER Books, National Bureau of Economic Research, Inc, number mill27-1, May.
  4. 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.
  5. Yannick Malevergne & Didier Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Post-Print hal-00520539, HAL.
  6. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
  7. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
  8. 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.
  9. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
  10. 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.
  11. 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.
  12. repec:wop:humbsf:2002-32 is not listed on IDEAS
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Cited by:
  1. Heinen, Andreas & Rengifo, Erick, 2007. "Multivariate autoregressive modeling of time series count data using copulas," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 564-583, September.
  2. Jesus Gonzalo & Jose Olmo, 2007. "The impact of heavy tails and comovements in downside-risk diversification," Economics Working Papers we20070208, Universidad Carlos III, Departamento de Economía.
  3. Andrew J. Patton, 2006. "Estimation of multivariate models for time series of possibly different lengths," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(2), pages 147-173.
  4. repec:hal:cesptp:halshs-00492124 is not listed on IDEAS
  5. repec:hal:cesptp:halshs-00645799 is not listed on IDEAS
  6. Dominique Guegan & Pierre-André Maugis, 2010. "An Econometric Study of Vine Copulas," Documents de travail du Centre d'Economie de la Sorbonne 10040, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  7. Okhrin, Ostap & Okhrin, Yarema & Schmid, Wolfgang, 2013. "On the structure and estimation of hierarchical Archimedean copulas," Journal of Econometrics, Elsevier, vol. 173(2), pages 189-204.
  8. Grundke, Peter & Polle, Simone, 2012. "Crisis and risk dependencies," European Journal of Operational Research, Elsevier, vol. 223(2), pages 518-528.
  9. Ostap Okhrin, 2010. "Fitting high-dimensional Copulae to Data," SFB 649 Discussion Papers SFB649DP2010-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  10. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. III," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 24(4), pages 100-130.
  11. Li, Lihui & Wen, Tao, 2013. "Estimation of C-MGARCH models based on the MBP method," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 665-673.
  12. Leonidas Tsiaras, 2010. "Dynamic Models of Exchange Rate Dependence Using Option Prices and Historical Returns," CREATES Research Papers 2010-35, School of Economics and Management, University of Aarhus.
  13. Wolfgang Härdle & Ostap Okhrin, 2010. "De copulis non est disputandum," AStA Advances in Statistical Analysis, Springer, vol. 94(1), pages 1-31, March.
  14. Roch, Oriol & Alegre, Antonio, 2006. "Testing the bivariate distribution of daily equity returns using copulas. An application to the Spanish stock market," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1312-1329, November.

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