IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v159y2017icp111-133.html
   My bibliography  Save this article

Score tests for covariate effects in conditional copulas

Author

Listed:
  • Gijbels, Irène
  • Omelka, Marek
  • Pešta, Michal
  • Veraverbeke, Noël

Abstract

We consider copula modeling of the dependence between two or more random variables in the presence of a multivariate covariate. The dependence parameter of the conditional copula possibly depends on the value of the covariate vector. In this paper we develop a new testing methodology for some important parametric specifications of this dependence parameter: constant, linear, quadratic, etc. in the covariate values, possibly after transformation with a link function. The margins are left unspecified. Our novel methodology opens plenty of new possibilities for testing how the conditional copula depends on the multivariate covariate and also for variable selection in copula model building. The suggested test is based on a Rao-type score statistic and regularity conditions are given under which the test has a limiting chi-square distribution under the null hypothesis. For small and moderate sample sizes, a permutation procedure is suggested to assess significance. In simulations it is shown that the test performs well (even under misspecification of the copula family and/or the dependence parameter structure) in comparison to available tests designed for testing for constancy of the dependence parameter. The test is illustrated on a real data set on concentrations of chemicals in water samples.

Suggested Citation

  • Gijbels, Irène & Omelka, Marek & Pešta, Michal & Veraverbeke, Noël, 2017. "Score tests for covariate effects in conditional copulas," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 111-133.
    • Handle: RePEc:eee:jmvana:v:159:y:2017:i:c:p:111-133
    DOI: 10.1016/j.jmva.2017.05.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X17302683
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2017.05.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo, 2010. "On the simplified pair-copula construction -- Simply useful or too simplistic?," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1296-1310, May.
    2. Elif F. Acar & Radu V. Craiu & Fang Yao, 2011. "Dependence Calibration in Conditional Copulas: A Nonparametric Approach," Biometrics, The International Biometric Society, vol. 67(2), pages 445-453, June.
    3. 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, May.
    4. Gijbels, Irène & Veraverbeke, Noël & Omelka, Marel, 2011. "Conditional copulas, association measures and their applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1919-1932, May.
    5. Acar, Elif F. & Genest, Christian & Nešlehová, Johanna, 2012. "Beyond simplified pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 74-90.
    6. Abegaz, Fentaw & Gijbels, Irène & Veraverbeke, Noël, 2012. "Semiparametric estimation of conditional copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 43-73.
    7. Kojadinovic, Ivan & Yan, Jun, 2010. "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i09).
    8. Irène Gijbels & Marek Omelka & Noël Veraverbeke, 2015. "Estimation of a Copula when a Covariate Affects only Marginal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1109-1126, December.
    9. Noël Veraverbeke & Marek Omelka & Irène Gijbels, 2011. "Estimation of a Conditional Copula and Association Measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(4), pages 766-780, December.
    10. Stöber, Jakob & Joe, Harry & Czado, Claudia, 2013. "Simplified pair copula constructions—Limitations and extensions," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 101-118.
    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. Martin Hrba & Matúš Maciak & Barbora Peštová & Michal Pešta, 2022. "Bootstrapping Not Independent and Not Identically Distributed Data," Mathematics, MDPI, vol. 10(24), pages 1-26, December.
    2. Neumeyer, Natalie & Omelka, Marek & Hudecová, Šárka, 2019. "A copula approach for dependence modeling in multivariate nonparametric time series," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 139-162.
    3. Gijbels, Irène & Omelka, Marek & Veraverbeke, Noël, 2021. "Omnibus test for covariate effects in conditional copula models," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    4. Adriana Csikosova & Maria Janoskova & Katarina Culkova, 2020. "Application of Discriminant Analysis for Avoiding the Risk of Quarry Operation Failure," JRFM, MDPI, vol. 13(10), pages 1-14, September.
    5. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.
    6. Marek Omelka & Šárka Hudecová & Natalie Neumeyer, 2021. "Maximum pseudo‐likelihood estimation based on estimated residuals in copula semiparametric models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1433-1473, December.
    7. Gijbels Irène & Matterne Margot, 2021. "Study of partial and average conditional Kendall’s tau," Dependence Modeling, De Gruyter, vol. 9(1), pages 82-120, January.
    8. Mat'uv{s} Maciak & Ostap Okhrin & Michal Pev{s}ta, 2018. "Dynamic and granular loss reserving with copulae," Papers 1801.01792, arXiv.org.

    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. Grazian, Clara & Dalla Valle, Luciana & Liseo, Brunero, 2022. "Approximate Bayesian conditional copulas," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    2. Derumigny Alexis & Fermanian Jean-David, 2017. "About tests of the “simplifying” assumption for conditional copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 154-197, August.
    3. Portier, François & Segers, Johan, 2018. "On the weak convergence of the empirical conditional copula under a simplifying assumption," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 160-181.
    4. Gijbels Irène & Matterne Margot, 2021. "Study of partial and average conditional Kendall’s tau," Dependence Modeling, De Gruyter, vol. 9(1), pages 82-120, January.
    5. Kajal Lahiri & Liu Yang, 2023. "Predicting binary outcomes based on the pair-copula construction," Empirical Economics, Springer, vol. 64(6), pages 3089-3119, June.
    6. Levi, Evgeny & Craiu, Radu V., 2018. "Bayesian inference for conditional copulas using Gaussian Process single index models," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 115-134.
    7. Fermanian, Jean-David & Lopez, Olivier, 2018. "Single-index copulas," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 27-55.
    8. Irène Gijbels & Marek Omelka & Noël Veraverbeke, 2015. "Estimation of a Copula when a Covariate Affects only Marginal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1109-1126, December.
    9. Zhu, Kailun & Kurowicka, Dorota & Nane, Gabriela F., 2021. "Simplified R-vine based forward regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    10. Derumigny Alexis & Fermanian Jean-David, 2019. "On kernel-based estimation of conditional Kendall’s tau: finite-distance bounds and asymptotic behavior," Dependence Modeling, De Gruyter, vol. 7(1), pages 292-321, January.
    11. Craiu, V. Radu & Sabeti, Avideh, 2012. "In mixed company: Bayesian inference for bivariate conditional copula models with discrete and continuous outcomes," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 106-120.
    12. Nagler, Thomas & Czado, Claudia, 2016. "Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 69-89.
    13. Bianchi, Pascal & Elgui, Kevin & Portier, François, 2023. "Conditional independence testing via weighted partial copulas," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    14. BenSaïda, Ahmed, 2018. "The contagion effect in European sovereign debt markets: A regime-switching vine copula approach," International Review of Financial Analysis, Elsevier, vol. 58(C), pages 153-165.
    15. Jean-David Fermanian & Olivier Lopez, 2015. "Single-index copulae," Working Papers 2015-12, Center for Research in Economics and Statistics.
    16. Abegaz, Fentaw & Gijbels, Irène & Veraverbeke, Noël, 2012. "Semiparametric estimation of conditional copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 43-73.
    17. Emura, Takeshi & Lai, Ching-Chieh & Sun, Li-Hsien, 2023. "Change point estimation under a copula-based Markov chain model for binomial time series," Econometrics and Statistics, Elsevier, vol. 28(C), pages 120-137.
    18. Derumigny, Alexis & Fermanian, Jean-David, 2020. "On Kendall’s regression," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    19. Zongwu Cai & Guannan Liu & Wei Long & Xuelong Luo, 2024. "Semiparametric Conditional Mixture Copula Models with Copula Selection," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202401, University of Kansas, Department of Economics, revised Jan 2024.
    20. Stöber, Jakob & Joe, Harry & Czado, Claudia, 2013. "Simplified pair copula constructions—Limitations and extensions," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 101-118.

    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:eee:jmvana:v:159:y:2017:i:c:p:111-133. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.