IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v63y2022i5d10.1007_s00362-021-01277-6.html
   My bibliography  Save this article

A goodness-of-fit test for copulas based on the collision test

Author

Listed:
  • Yiran Chen

    (Florida State University)

  • Giray Ökten

    (Florida State University)

Abstract

We propose a new goodness-of-fit test for copulas using the collision test for pseudorandom number generators and Voronoi diagrams generated by low-discrepancy sequences. We provide an error bound for numerical integration that involves number of collisions when the unit cube is partitioned via Voronoi cells, and present an example from option pricing. We investigate the accuracy of the goodness-of-fit test numerically, and compare it with three tests in the literature. The numerical results suggest the new test excels in computationally demanding scenarios when the sample size is large or computing the copula is expensive, and provides sufficient accuracy in computing times that are faster by factors of thousands than the tests with comparable accuracy.

Suggested Citation

  • Yiran Chen & Giray Ökten, 2022. "A goodness-of-fit test for copulas based on the collision test," Statistical Papers, Springer, vol. 63(5), pages 1369-1385, October.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:5:d:10.1007_s00362-021-01277-6
    DOI: 10.1007/s00362-021-01277-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-021-01277-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-021-01277-6?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. 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.
    2. 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.
    3. 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.
    4. Christian Genest & Jean‐François Quessy & Bruno Rémillard, 2006. "Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366, June.
    5. Panchenko, Valentyn, 2005. "Goodness-of-fit test for copulas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 176-182.
    6. Marsaglia, George & Tsang, Wai Wan, 2000. "The Ziggurat Method for Generating Random Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i08).
    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. Okten, Giray & Eastman, Warren, 2004. "Randomized quasi-Monte Carlo methods in pricing securities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2399-2426, December.
    9. Leong, Philip H. W. & Zhang, Ganglie & Lee, Dong-U & Luk, Wayne & Villasenor, John, 2005. "A Comment on the Implementation of the Ziggurat Method," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i07).
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    3. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2010. "Out-of-sample comparison of copula specifications in multivariate density forecasts," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1596-1609, September.
    4. Weiß, Gregor N.F., 2011. "Are Copula-GoF-tests of any practical use? Empirical evidence for stocks, commodities and FX futures," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(2), pages 173-188, May.
    5. Can, S.U. & Einmahl, John & Laeven, R.J.A., 2020. "Goodness-of-fit testing for copulas: A distribution-free approach," Other publications TiSEM 211b2be9-b46e-41e2-9b95-1, Tilburg University, School of Economics and Management.
    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. Grundke, Peter & Polle, Simone, 2012. "Crisis and risk dependencies," European Journal of Operational Research, Elsevier, vol. 223(2), pages 518-528.
    8. 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.
    9. Gregor Weiß, 2013. "Copula-GARCH versus dynamic conditional correlation: an empirical study on VaR and ES forecasting accuracy," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 179-202, August.
    10. Can, S.U. & Einmahl, John & Laeven, R.J.A., 2017. "Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas," Other publications TiSEM feb9a064-2a9f-47d6-a02b-7, Tilburg University, School of Economics and Management.
    11. Can, S.U. & Einmahl, John & Laeven, R.J.A., 2017. "Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas," Other publications TiSEM feb9a064-2a9f-47d6-a02b-7, Tilburg University, School of Economics and Management.
    12. Brodsky, Boris & Penikas, Henry & Safaryan, Irina, 2009. "Detection of Structural Breaks in Copula Models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 16(4), pages 3-15.
    13. 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.
    14. Boris Brodsky & Henry Penikas & Irina Safaryan, 2012. "Copula structural shift identification," HSE Working papers WP BRP 05/FE/2012, National Research University Higher School of Economics.
    15. Bentoumi Rachid & Mesfioui Mhamed & Alvo Mayer, 2019. "Dependence measure for length-biased survival data using copulas," Dependence Modeling, De Gruyter, vol. 7(1), pages 348-364, January.
    16. 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.
    17. Marc Gronwald & Janina Ketterer & Stefan Trück, 2011. "The Dependence Structure between Carbon Emission Allowances and Financial Markets - A Copula Analysis," CESifo Working Paper Series 3418, CESifo.
    18. Wanling Huang & Artem Prokhorov, 2014. "A Goodness-of-fit Test for Copulas," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 751-771, October.
    19. 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.
    20. Roch, Oriol & Alegre, Antonio, 2006. "Testing the bivariate distribution of daily equity returns using copulas. An application to the Spanish stock market," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1312-1329, November.

    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:spr:stpapr:v:63:y:2022:i:5:d:10.1007_s00362-021-01277-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.