Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2013-041.html
   My bibliography  Save this paper

Goodness-of-fit test for specification of semiparametric copula dependence models

Author

Listed:
  • Zhang, Shulin
  • Okhrin, Ostap
  • Zhou, Qian M.
  • Song, Peter X.-K.
Abstract
This paper concerns goodness-of-fit test for semiparametric copula models. Our contribution is two-fold: we first propose a new test constructed via the comparison between in-sample and out-of-sample pseudolikelihoods, which avoids the use of any probability integral transformations. Under the null hypothesis that the copula model is correctly specified, we show that the proposed test statistic converges in probability to a constant equal to the dimension of the parameter space and establish the asymptotic normality for the test. Second, we introduce a hybrid mechanism to combine several test statistics, so that the resulting test will make a desirable test power among the involved tests. This hybrid method is particularly appealing when there exists no single dominant optimal test. We conduct comprehensive simulation experiments to compare the proposed new test and hybrid approach with the best blank test shown in Genest et al. (2009). For illustration, we apply the proposed tests to analyze three real datasets.

Suggested Citation

  • Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2013. "Goodness-of-fit test for specification of semiparametric copula dependence models," SFB 649 Discussion Papers 2013-041, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2013-041
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/91594/1/SFB649DP2013-041.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 1-14.
    2. Wanling Huang & Artem Prokhorov, 2014. "A Goodness-of-fit Test for Copulas," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 751-771, October.
    3. Panchenko, Valentyn, 2005. "Goodness-of-fit test for copulas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 176-182.
    4. Cipollini, Fabrizio & Gallo, Giampiero M., 2010. "Automated variable selection in vector multiplicative error models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2470-2486, November.
    5. Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
    6. Peter Xue‐Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320, June.
    7. Daniel Berg & Jean‐François Quessy, 2009. "Local Power Analyses of Goodness‐of‐fit Tests for Copulas," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 389-412, September.
    8. 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.
    9. Raffaella Giacomini & Barbara Rossi, 2009. "Detecting and Predicting Forecast Breakdowns," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(2), pages 669-705.
    10. 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.
    11. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    12. 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.
    13. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    14. 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.
    15. Okhrin, Ostap & Okhrin, Yarema & Schmid, Wolfgang, 2009. "Properties of hierarchical Archimedean copulas," SFB 649 Discussion Papers 2009-014, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    16. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    17. Peter J. Danaher & Michael S. Smith, 2011. "Modeling Multivariate Distributions Using Copulas: Applications in Marketing," Marketing Science, INFORMS, vol. 30(1), pages 4-21, 01-02.
    18. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
    19. Presnell, Brett & Boos, Dennis D., 2004. "The IOS Test for Model Misspecification," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 216-227, January.
    20. Nikolaus Hautsch, 2012. "Econometrics of Financial High-Frequency Data," Springer Books, Springer, number 978-3-642-21925-2, January.
    21. Peter X.-K. Song & Mingyao Li & Ying Yuan, 2009. "Joint Regression Analysis of Correlated Data Using Gaussian Copulas," Biometrics, The International Biometric Society, vol. 65(1), pages 60-68, March.
    22. Didier Cossin & Henry Schellhorn, 2007. "Credit Risk in a Network Economy," Management Science, INFORMS, vol. 53(10), pages 1604-1617, October.
    23. Christian M. Hafner & Hans Manner, 2012. "Dynamic stochastic copula models: estimation, inference and applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(2), pages 269-295, March.
    24. 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.
    25. Qian M. Zhou & Peter X.-K. Song & Mary E. Thompson, 2012. "Information Ratio Test for Model Misspecification in Quasi-Likelihood Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 205-213, March.
    26. Olivier Scaillet, 2005. "A Kolmogorov-Smirnov Type Test for Positive Quadrant Dependence," FAME Research Paper Series rp128, International Center for Financial Asset Management and Engineering.
    27. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    28. 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.
    29. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    30. Okhrin Ostap & Okhrin Yarema & Schmid Wolfgang, 2013. "Properties of hierarchical Archimedean copulas," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 21-54, March.
    31. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    32. Dobric, Jadran & Schmid, Friedrich, 2007. "A goodness of fit test for copulas based on Rosenblatt's transformation," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4633-4642, May.
    33. Freedman, David A., 2009. "Diagnostics cannot have much power against general alternatives," International Journal of Forecasting, Elsevier, vol. 25(4), pages 833-839, October.
    34. Zhang, Shulin & Song, Peter X.-K. & Shi, Daimin & Zhou, Qian M., 2012. "Information ratio test for model misspecification on parametric structures in stochastic diffusion models," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3975-3987.
    35. Michel Denuit, 2004. "Nonparametric Tests for Positive Quadrant Dependence," Journal of Financial Econometrics, Oxford University Press, vol. 2(3), pages 422-450.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tao Sun & Yu Cheng & Ying Ding, 2023. "An information ratio‐based goodness‐of‐fit test for copula models on censored data," Biometrics, The International Biometric Society, vol. 79(3), pages 1713-1725, September.
    2. Jie Huang & Haiming Zhou & Nader Ebrahimi, 2022. "Bayesian Bivariate Cure Rate Models Using Copula Functions," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(3), pages 1-9, May.
    3. F. Marta L. Di Lascio & Andrea Menapace & Maurizio Righetti, 2020. "Joint and conditional dependence modelling of peak district heating demand and outdoor temperature: a copula-based approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 373-395, June.
    4. Shulin Zhang & Qian M. Zhou & Huazhen Lin, 2021. "Goodness-of-fit test of copula functions for semi-parametric univariate time series models," Statistical Papers, Springer, vol. 62(4), pages 1697-1721, August.
    5. Poeschel, Friedrich, 2012. "Assortative matching through signals," VfS Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62061, Verein für Socialpolitik / German Economic Association.
    6. Fontaine, Charles & Frostig, Ron D. & Ombao, Hernando, 2020. "Modeling non-linear spectral domain dependence using copulas with applications to rat local field potentials," Econometrics and Statistics, Elsevier, vol. 15(C), pages 85-103.
    7. Klochkov, Yegor & Härdle, Wolfgang Karl & Xu, Xiu, 2019. "Localizing Multivariate CAViaR," IRTG 1792 Discussion Papers 2019-007, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    8. Bingduo Yang & Zongwu Cai & Christian M. Hafner & Guannan Liu, 2018. "Trending Mixture Copula Models with Copula Selection," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201809, University of Kansas, Department of Economics, revised Sep 2018.
    9. Tao Sun & Yi Liu & Richard J. Cook & Wei Chen & Ying Ding, 2019. "Copula-based score test for bivariate time-to-event data, with application to a genetic study of AMD progression," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 546-568, July.
    10. Miriam Jaser & Aleksey Min, 2021. "On tests for symmetry and radial symmetry of bivariate copulas towards testing for ellipticity," Computational Statistics, Springer, vol. 36(3), pages 1-26, September.
    11. Gong Chen & Hartmut Fricke & Ostap Okhrin & Judith Rosenow, 2022. "Importance of Weather Conditions in a Flight Corridor," Stats, MDPI, vol. 5(1), pages 1-27, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:hum:wpaper:sfb649dp2013-041 is not listed on IDEAS
    2. Shulin Zhang & Qian M. Zhou & Huazhen Lin, 2021. "Goodness-of-fit test of copula functions for semi-parametric univariate time series models," Statistical Papers, Springer, vol. 62(4), pages 1697-1721, August.
    3. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    4. Wanling Huang & Artem Prokhorov, 2014. "A Goodness-of-fit Test for Copulas," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 751-771, October.
    5. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. III," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 24(4), pages 100-130.
    6. Kajal Lahiri & Liu Yang, 2023. "Predicting binary outcomes based on the pair-copula construction," Empirical Economics, Springer, vol. 64(6), pages 3089-3119, June.
    7. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    8. 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.
    9. Bruno Rémillard, 2017. "Goodness-of-Fit Tests for Copulas of Multivariate Time Series," Econometrics, MDPI, vol. 5(1), pages 1-23, March.
    10. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    11. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    12. 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.
    13. Juan Lin & Ximing Wu, 2015. "Smooth Tests of Copula Specifications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 128-143, January.
    14. Lu, Xiaohui & Zheng, Xu, 2020. "A goodness-of-fit test for copulas based on martingale transformation," Journal of Econometrics, Elsevier, vol. 215(1), pages 84-117.
    15. Bücher, Axel & Dette, Holger, 2010. "Some comments on goodness-of-fit tests for the parametric form of the copula based on L2-distances," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 749-763, March.
    16. Hautsch, Nikolaus & Okhrin, Ostap & Ristig, Alexander, 2012. "Modeling time-varying dependencies between positive-valued high-frequency time series," SFB 649 Discussion Papers 2012-054, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    17. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    18. repec:hum:wpaper:sfb649dp2012-054 is not listed on IDEAS
    19. Kjersti Aas, 2016. "Pair-Copula Constructions for Financial Applications: A Review," Econometrics, MDPI, vol. 4(4), pages 1-15, October.
    20. Amjad, Muhammad & Akbar, Muhammad & Ullah, Hamd, 2022. "A copula-based approach for creating an index of micronutrient intakes at household level in Pakistan," Economics & Human Biology, Elsevier, vol. 46(C).
    21. Penikas, H., 2010. "Financial Applications of Copula-Models," Journal of the New Economic Association, New Economic Association, issue 7, pages 24-44.
    22. Grundke, Peter & Polle, Simone, 2012. "Crisis and risk dependencies," European Journal of Operational Research, Elsevier, vol. 223(2), pages 518-528.

    More about this item

    Keywords

    hybrid test; in-and-out-of sample likelihood; power; tail dependence;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:sfb649:sfb649dp2013-041. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.