IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2015-12.html
   My bibliography  Save this paper

Single-index copulae

Author

Listed:
  • Jean-David Fermanian

    (CREST, Laboratoire de Finance et d’Assurance)

  • Olivier Lopez

    (CREST, Laboratoire de Finance et d’Assurance)

Abstract

We introduce so-called "single-index copulae". They are semi-parametric conditional copulae whose parameter is an unknown "link" function of a univariate index only. We provide estimates of this link function and of the ?nite dimensional unknown parameter. The asymptotic properties of the latter estimates are stated. Thanks to some properties of conditional Kendall’s tau, we illustrate our technical conditions with several usual copula families.

Suggested Citation

  • Jean-David Fermanian & Olivier Lopez, 2015. "Single-index copulae," Working Papers 2015-12, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2015-12
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2015-12.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    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. Lopez, Olivier & Patilea, Valentin & Van Keilegom, Ingrid, 2013. "Single index regression models in the presence of censoring depending on the covariates," LIDAM Reprints ISBA 2013029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate extensions of Spearman's rho and related statistics," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 407-416, February.
    5. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    6. 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.
    7. 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.
    8. 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.
    9. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    10. Fermanian, Jean-David & Wegkamp, Marten H., 2012. "Time-dependent copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 19-29.
    11. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    12. Jondeau, Eric & Rockinger, Michael, 2006. "The Copula-GARCH model of conditional dependencies: An international stock market application," Journal of International Money and Finance, Elsevier, vol. 25(5), pages 827-853, August.
    13. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    14. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.
    15. 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.
    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. Fermanian, Jean-David & Lopez, Olivier, 2018. "Single-index copulas," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 27-55.
    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. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    4. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    5. 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.
    6. Grazian, Clara & Dalla Valle, Luciana & Liseo, Brunero, 2022. "Approximate Bayesian conditional copulas," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    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. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    9. Derumigny, Alexis & Fermanian, Jean-David, 2019. "A classification point-of-view about conditional Kendall’s tau," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 70-94.
    10. Vatter, Thibault & Chavez-Demoulin, Valérie, 2015. "Generalized additive models for conditional dependence structures," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 147-167.
    11. Acar, Elif F. & Czado, Claudia & Lysy, Martin, 2019. "Flexible dynamic vine copula models for multivariate time series data," Econometrics and Statistics, Elsevier, vol. 12(C), pages 181-197.
    12. Lahiri, Kajal & Yang, Liu, 2013. "Forecasting Binary Outcomes," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1025-1106, Elsevier.
    13. 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.
    14. Kajal Lahiri & Liu Yang, 2023. "Predicting binary outcomes based on the pair-copula construction," Empirical Economics, Springer, vol. 64(6), pages 3089-3119, June.
    15. Grundke, Peter & Polle, Simone, 2012. "Crisis and risk dependencies," European Journal of Operational Research, Elsevier, vol. 223(2), pages 518-528.
    16. 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.
    17. Hofert, Marius & Prasad, Avinash & Zhu, Mu, 2022. "Multivariate time-series modeling with generative neural networks," Econometrics and Statistics, Elsevier, vol. 23(C), pages 147-164.
    18. Philippas, Dionisis & Siriopoulos, Costas, 2013. "Putting the “C” into crisis: Contagion, correlations and copulas on EMU bond markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 27(C), pages 161-176.
    19. Albulescu, Claudiu Tiberiu & Aubin, Christian & Goyeau, Daniel & Tiwari, Aviral Kumar, 2018. "Extreme co-movements and dependencies among major international exchange rates: A copula approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 69(C), pages 56-69.
    20. Lu Lu & Sujit Ghosh, 2024. "Nonparametric Estimation of Conditional Copula Using Smoothed Checkerboard Bernstein Sieves," Mathematics, MDPI, vol. 12(8), pages 1-17, April.

    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:crs:wpaper:2015-12. 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: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.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.