IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v71y2009i3p737-753.html
   My bibliography  Save this article

Copula structure analysis

Author

Listed:
  • Claudia Klüppelberg
  • Gabriel Kuhn

Abstract

Summary. We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulas a correlation‐like structure remains, but different margins and non‐existence of moments are possible. After introducing the new concept and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behaviour of the statistics can be observed even for small sample sizes. Finally, we show our method at work for a financial data set and explain differences between our copula‐based approach and the classical approach. Our new method yielear models also.

Suggested Citation

  • Claudia Klüppelberg & Gabriel Kuhn, 2009. "Copula structure analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 737-753, June.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:3:p:737-753
    DOI: 10.1111/j.1467-9868.2009.00707.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9868.2009.00707.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9868.2009.00707.x?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
    ---><---

    References listed on IDEAS

    as
    1. B. Praag & T. Dijkstra & J. Velzen, 1985. "Least-squares theory based on general distributional assumptions with an application to the incomplete observations problem," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 25-36, March.
    2. Panchenko, Valentyn, 2005. "Goodness-of-fit test for copulas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 176-182.
    3. James Steiger & Alexander Shapiro & Michael Browne, 1985. "On the multivariate asymptotic distribution of sequential Chi-square statistics," Psychometrika, Springer;The Psychometric Society, vol. 50(3), pages 253-263, September.
    4. Manzotti, A. & Pérez, Francisco J. & Quiroz, Adolfo J., 2002. "A Statistic for Testing the Null Hypothesis of Elliptical Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 274-285, May.
    5. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    6. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    7. Albert Satorra & Peter Bentler, 2001. "A scaled difference chi-square test statistic for moment structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 507-514, December.
    8. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
    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. Dong Hwan Oh & Andrew J. Patton, 2017. "Modeling Dependence in High Dimensions With Factor Copulas," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 139-154, January.
    2. Langworthy, Benjamin W. & Stephens, Rebecca L. & Gilmore, John H. & Fine, Jason P., 2021. "Canonical correlation analysis for elliptical copulas," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    3. Segers, Johan & van den Akker, Ramon & Werker, Bas, 2013. "Semiparametric Gaussian copula models: Geometry and efficient rank-based Estimation," LIDAM Discussion Papers ISBA 2013030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Yu, Long & He, Yong & Zhang, Xinsheng, 2019. "Robust factor number specification for large-dimensional elliptical factor model," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    5. Krupskii, Pavel & Joe, Harry, 2013. "Factor copula models for multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 85-101.
    6. Šárka Hudecová & Miroslav Šiman, 2021. "Testing symmetry around a subspace," Statistical Papers, Springer, vol. 62(5), pages 2491-2508, October.
    7. Quessy, Jean-François & Durocher, Martin, 2019. "The class of copulas arising from squared distributions: Properties and inference," Econometrics and Statistics, Elsevier, vol. 12(C), pages 148-166.

    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. Albisetti, Isaia & Balabdaoui, Fadoua & Holzmann, Hajo, 2020. "Testing for spherical and elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    2. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    3. Valdez, Emiliano A. & Dhaene, Jan & Maj, Mateusz & Vanduffel, Steven, 2009. "Bounds and approximations for sums of dependent log-elliptical random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 385-397, June.
    4. 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.
    5. Mohamed Belalia & Jean-François Quessy, 2024. "Generalized simulated method-of-moments estimators for multivariate copulas," Statistical Papers, Springer, vol. 65(8), pages 4811-4841, October.
    6. Langworthy, Benjamin W. & Stephens, Rebecca L. & Gilmore, John H. & Fine, Jason P., 2021. "Canonical correlation analysis for elliptical copulas," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    7. Sancetta, A. & Nikanrova, A., 2005. "Forecasting and Prequential Validation for Time Varying Meta-Elliptical Distributions with a Study of Commodity Futures Prices," Cambridge Working Papers in Economics 0516, Faculty of Economics, University of Cambridge.
    8. Derumigny, A. & Fermanian, J.-D., 2022. "Identifiability and estimation of meta-elliptical copula generators," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    9. Bruno Rémillard, 2017. "Goodness-of-Fit Tests for Copulas of Multivariate Time Series," Econometrics, MDPI, vol. 5(1), pages 1-23, March.
    10. Dominique Guegan, 2007. "Global and local stationary modelling in finance: theory and empirical evidence," Post-Print halshs-00187875, HAL.
    11. Quessy, Jean-François & Durocher, Martin, 2019. "The class of copulas arising from squared distributions: Properties and inference," Econometrics and Statistics, Elsevier, vol. 12(C), pages 148-166.
    12. Zhang, Ran & Czado, Claudia & Min, Aleksey, 2011. "Efficient maximum likelihood estimation of copula based meta t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1196-1214, March.
    13. P. M. Bentler & Chih-Ping Chou, 1987. "Practical Issues in Structural Modeling," Sociological Methods & Research, , vol. 16(1), pages 78-117, August.
    14. Chen, Ray-Bing & Chen, Ying & Härdle, Wolfgang K., 2014. "TVICA—Time varying independent component analysis and its application to financial data," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 95-109.
    15. Abduraimova, Kumushoy, 2022. "Contagion and tail risk in complex financial networks," Journal of Banking & Finance, Elsevier, vol. 143(C).
    16. Josselin Garnier & Knut Sølna, 2018. "Option pricing under fast-varying and rough stochastic volatility," Annals of Finance, Springer, vol. 14(4), pages 489-516, November.
    17. Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters, 2006. "Random walks, liquidity molasses and critical response in financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 115-123.
    18. Juan C. Henao-Londono & Sebastian M. Krause & Thomas Guhr, 2021. "Price response functions and spread impact in correlated financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(4), pages 1-20, April.
    19. Westerhoff, Frank H. & Dieci, Roberto, 2006. "The effectiveness of Keynes-Tobin transaction taxes when heterogeneous agents can trade in different markets: A behavioral finance approach," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 293-322, February.
    20. Laura Vieten & Anne Marit Wöhrmann & Alexandra Michel, 2022. "Work-Time Control and Exhaustion: Internal Work-to-Home Interference and Internal Home-to-Work Interference as Mediators," IJERPH, MDPI, vol. 19(6), pages 1-17, March.

    More about this item

    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:bla:jorssb:v:71:y:2009:i:3:p:737-753. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.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.