IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v112y2017icp24-41.html
   My bibliography  Save this article

Some copula inference procedures adapted to the presence of ties

Author

Listed:
  • Kojadinovic, Ivan

Abstract

When modeling the distribution of a multivariate continuous random vector using the so-called copula approach, it is not uncommon to have ties in the coordinate samples of the available data because of rounding or lack of measurement precision. Yet, the vast majority of existing inference procedures on the underlying copula were both theoretically derived and practically implemented under the assumption of no ties. Applying them nonetheless can lead to strongly biased results. Some of the existing statistical tests can however be adapted to provide meaningful results in the presence of ties. It is the case of some tests of exchangeability, radial symmetry, extreme-value dependence and goodness of fit. Detailed algorithms for computing approximate p-values for the modified tests are provided and their finite-sample behaviors are empirically investigated through extensive Monte Carlo experiments. An illustration on a real-world insurance data set concludes the work.

Suggested Citation

  • Kojadinovic, Ivan, 2017. "Some copula inference procedures adapted to the presence of ties," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 24-41.
    • Handle: RePEc:eee:csdana:v:112:y:2017:i:c:p:24-41
    DOI: 10.1016/j.csda.2017.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947317300269
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2017.02.006?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. Kojadinovic, Ivan & Yan, Jun, 2010. "Nonparametric rank-based tests of bivariate extreme-value dependence," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2234-2249, October.
    2. Kojadinovic, Ivan & Segers, Johan & Yan, Jun, 2011. "Large-sample tests of extreme-value dependence for multivariate copulas," LIDAM Reprints ISBA 2011025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. 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.
    4. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    5. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    6. Christian Genest & Johanna Nešlehová, 2014. "On tests of radial symmetry for bivariate copulas," Statistical Papers, Springer, vol. 55(4), pages 1107-1119, November.
    7. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    8. Ivan Kojadinovic & Jun Yan, 2012. "A Non-parametric Test of Exchangeability for Extreme-Value and Left-Tail Decreasing Bivariate Copulas," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(3), pages 480-496, September.
    9. 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.
    10. Kojadinovic, Jean D. & Segers, Johan & Yan, Yun, 2011. "Large-sample tests of extreme-value dependence for multivariate copulas," LIDAM Discussion Papers ISBA 2011012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    12. Berghaus, Betina & Bücher, Axel, 2017. "Goodness-Of-Fit Tests For Multivariate Copula-Based Time Series Models," Econometric Theory, Cambridge University Press, vol. 33(2), pages 292-330, April.
    13. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
    14. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    15. 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).
    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. Punzo, Antonio & Bagnato, Luca, 2022. "Dimension-wise scaled normal mixtures with application to finance and biometry," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    2. Faugeras Olivier P., 2017. "Inference for copula modeling of discrete data: a cautionary tale and some facts," Dependence Modeling, De Gruyter, vol. 5(1), pages 121-132, January.
    3. Zhu, Junyi & Steiner, Viktor, 2020. "A Joint Top Income and Wealth Distribution," VfS Annual Conference 2020 (Virtual Conference): Gender Economics 224651, Verein für Socialpolitik / German Economic Association.
    4. Steiner, Viktor & Zhu, Junyi, 2021. "A joint top income and wealth distribution," Discussion Papers 2021/3, Free University Berlin, School of Business & Economics.

    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. Penikas, H., 2010. "Financial Applications of Copula-Models," Journal of the New Economic Association, New Economic Association, issue 7, pages 24-44.
    2. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    3. Mazo, Gildas & Girard, Stéphane & Forbes, Florence, 2015. "A class of multivariate copulas based on products of bivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 363-376.
    4. Bücher, Axel & Kojadinovic, Ivan & Rohmer, Tom & Segers, Johan, 2014. "Detecting changes in cross-sectional dependence in multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 111-128.
    5. Bücher Axel & Jaser Miriam & Min Aleksey, 2021. "Detecting departures from meta-ellipticity for multivariate stationary time series," Dependence Modeling, De Gruyter, vol. 9(1), pages 121-140, January.
    6. 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.
    7. 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.
    8. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
    9. Quessy, Jean-François, 2021. "A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    10. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
    11. Fang, Y. & Madsen, L., 2013. "Modified Gaussian pseudo-copula: Applications in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 292-301.
    12. Segers, Johan, 2012. "Nonparametric inference for max-stable dependence : Discussion of "Statistical Modelling of Spatial Extremes" by A. C. Davison, S. Padoan and M. Ribatet, to appear in Statistical Science," LIDAM Discussion Papers ISBA 2012012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Jean-David Fermanian & Dragan Radulovic & Marten Wegkamp, 2013. "A Asymptotic Total Variation Test for Copulas," Working Papers 2013-25, Center for Research in Economics and Statistics.
    14. Bucher, Axel & Kojadinovic, Ivan, 2013. "A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing," LIDAM Discussion Papers ISBA 2013029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Catalina Bolancé & Carlos Alberto Acuña, 2021. "A New Kernel Estimator of Copulas Based on Beta Quantile Transformations," Mathematics, MDPI, vol. 9(10), pages 1-16, May.
    16. 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.
    17. Kojadinovic, Jean D. & Segers, Johan & Yan, Yun, 2011. "Large-sample tests of extreme-value dependence for multivariate copulas," LIDAM Discussion Papers ISBA 2011012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Kojadinovic, Ivan & Yan, Jun, 2010. "Nonparametric rank-based tests of bivariate extreme-value dependence," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2234-2249, October.
    19. Jaser Miriam & Haug Stephan & Min Aleksey, 2017. "A simple non-parametric goodness-of-fit test for elliptical copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 330-353, December.
    20. Kiriliouk, Anna & Segers, Johan & Tsukahara, Hideatsu, 2019. "On Some Resampling Procedures with the Empirical Beta Copula," LIDAM Discussion Papers ISBA 2019012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    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:csdana:v:112:y:2017:i:c:p:24-41. 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/locate/csda .

    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.