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(IAM Series No 003) 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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  • Yanqin Fan
  • Xiaohong Chen
  • Andrew Patton

    ()

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 efficiency 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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File URL: http://www.lse.ac.uk/fmg/workingPapers/discussionPapers/fmgdps/dp483.pdf
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Bibliographic Info

Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp483.

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Date of creation: Feb 2004
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Handle: RePEc:fmg:fmgdps:dp483

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Web page: http://www.lse.ac.uk/fmg/

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Cited by:
  1. Xiaohong Chen & Yanqin Fan, 2002. "Estimation of Copula-Based Semiparametric Time Series Models," Vanderbilt University Department of Economics Working Papers 0226, Vanderbilt University Department of Economics, revised Oct 2004.
  2. Yanqin Fan & Xiaohong Chen, 2004. "Estimation of Copula-Based Semiparametric Time Series Models," Econometric Society 2004 Far Eastern Meetings 559, Econometric Society.
  3. Oriol Roch Casellas & Antonio Alegre Escolano, 2005. "Testing the bivariate distribution of daily equity returns using copulas. An application to the Spanish stock market," Working Papers in Economics 143, Universitat de Barcelona. Espai de Recerca en Economia.
  4. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
  5. Jonathan B. Hill, 2005. "Gaussian Tests of "Extremal White Noise" for Dependent, Heterogeneous, Heavy Tailed Strochastic Processes with an Application," Working Papers 0513, Florida International University, Department of Economics.
  6. Panchenko, V., 2004. "Goodness-of-fit test for copulas," CeNDEF Working Papers 04-16, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  7. Xiaohong Chen & Yanqin Fan, 2004. "Estimation and Model Selection of Semiparametric Copula-Based Multivariate Dynamic Models under Copula Misspecification," Vanderbilt University Department of Economics Working Papers 0419, Vanderbilt University Department of Economics, revised Sep 2004.

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