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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

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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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  • Yanqin Fan & Xiaohong Chen & Andrew Patton, 2004. "(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," FMG Discussion Papers dp483, Financial Markets Group.
  • Handle: RePEc:fmg:fmgdps:dp483
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    Cited by:

    1. Panchenko, Valentyn, 2005. "Goodness-of-fit test for copulas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 176-182.
    2. Matthias Fischer & Christian Köck, "undated". "Multivariate Copula Models at Work: Dependence Structure of Energie Prices," Energy and Environmental Modeling 2007 24000014, EcoMod.
    3. Xiangdong Long & Liangjun Su & Aman Ullah, 2011. "Estimation and Forecasting of Dynamic Conditional Covariance: A Semiparametric Multivariate Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 109-125, January.
    4. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    5. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
    6. Mitchell, James, 2013. "The Recalibrated and Copula Opinion Pools," EMF Research Papers 02, Economic Modelling and Forecasting Group.
    7. Sim, Nicholas, 2016. "Modeling the dependence structures of financial assets through the Copula Quantile-on-Quantile approach," International Review of Financial Analysis, Elsevier, vol. 48(C), pages 31-45.
    8. Mark Trede & Cornelia Savu, 2013. "Do stock returns have an Archimedean copula?," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(8), pages 1764-1778, August.
    9. 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.
    10. 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.
    11. Scaillet, Olivier, 2007. "Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 533-543, March.

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