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A Goodness-of-fit Test for Copulas

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Abstract

A new goodness-of-fit test of copulas is proposed. It is based on restrictions on certain elements of the information matrix and so relates to the White (1982) specification test. The test avoids the need to correctly specify and consistently estimate a parametric model for the marginal distributions. It does not involve kernel weighting and bandwidth selection or parametric bootstrap and is relatively simple compared to other available tests.

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Paper provided by Concordia University, Department of Economics in its series Working Papers with number 10002.

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Date of creation: Apr 2010
Date of revision: Apr 2010
Handle: RePEc:crd:wpaper:10002
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  • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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  1. Taylor, Larry W., 1987. "The size bias of White's information matrix test," Economics Letters, Elsevier, vol. 24(1), pages 63-67.
  2. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
  3. Murray D. Smith, 2003. "Modelling sample selection using Archimedean copulas," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 99-123, 06.
  4. Panchenko, Valentyn, 2005. "Goodness-of-fit test for copulas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 176-182.
  5. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
  6. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48.
  7. Daniel Berg, 2009. "Copula goodness-of-fit testing: an overview and power comparison," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 675-701.
  8. Prokhorov, Artem & Schmidt, Peter, 2009. "Likelihood-based estimation in a panel setting: Robustness, redundancy and validity of copulas," Journal of Econometrics, Elsevier, vol. 153(1), pages 93-104, November.
  9. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
  10. Davidson, Russell & MacKinnon, James G, 1992. "A New Form of the Information Matrix Test," Econometrica, Econometric Society, vol. 60(1), pages 145-157, January.
  11. Klugman, Stuart A. & Parsa, Rahul, 1999. "Fitting bivariate loss distributions with copulas," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 139-148, March.
  12. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
  13. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 566-584, December.
  14. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, 05.
  15. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  16. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
  17. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
  18. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
  19. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-1053, July.
  20. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
  21. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
  22. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
  23. Hall, Alastair, 1989. "On the calculation of the information matrix test in the normal linear regression model," Economics Letters, Elsevier, vol. 29(1), pages 31-35.
  24. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
  25. Yanqin Fan & Xiaohong Chen, 2004. "Estimation of Copula-Based Semiparametric Time Series Models," Econometric Society 2004 Far Eastern Meetings 559, Econometric Society.
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Cited by:

  1. Ding, Wei & Song, Peter X.-K., 2016. "EM algorithm in Gaussian copula with missing data," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 1-11.
  2. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
  3. Nguyen, Cuong & Bhatti, M. Ishaq & Komorníková, Magda & Komorník, Jozef, 2016. "Gold price and stock markets nexus under mixed-copulas," Economic Modelling, Elsevier, vol. 58(C), pages 283-292.
  4. Schepsmeier, Ulf, 2015. "Efficient information based goodness-of-fit tests for vine copula models with fixed margins: A comprehensive review," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 34-52.
  5. repec:eee:phsmap:v:480:y:2017:i:c:p:10-21 is not listed on IDEAS
  6. Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2016. "Goodness-of-fit test for specification of semiparametric copula dependence models," Journal of Econometrics, Elsevier, vol. 193(1), pages 215-233.
  7. Huang, Wanling & Mollick, André Varella & Nguyen, Khoa Huu, 2016. "U.S. stock markets and the role of real interest rates," The Quarterly Review of Economics and Finance, Elsevier, vol. 59(C), pages 231-242.
  8. Kjersti Aas, 2016. "Pair-Copula Constructions for Financial Applications: A Review," Econometrics, MDPI, Open Access Journal, vol. 4(4), pages 1-15, October.
  9. Shulin Zhang, & Ostap Okhrin, & Qian M. Zhou & Peter X.-K. Song, 2013. "Goodness-of-fit Test for Specification of Semiparametric Copula Dependence Models," SFB 649 Discussion Papers SFB649DP2013-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  10. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2016. "Generalized Information Matrix Tests for Detecting Model Misspecification," Econometrics, MDPI, Open Access Journal, vol. 4(4), pages 1-24, November.
  11. Okhrin Ostap, 2013. "Editorial to the special issue on Copulae of Statistics & Risk Modeling," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 281-286, December.

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