IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v32y2005i4p387-407.html
   My bibliography  Save this article

Nonparametric estimation of the lower tail dependence λL in bivariate copulas

Author

Listed:
  • Jadran Dobric
  • Friedrich Schmid

Abstract

The lower tail dependence λL is a measure that characterizes the tendency of extreme co-movements in the lower tails of a bivariate distribution. It is invariant with respect to strictly increasing transformations of the marginal distribution and is therefore a function of the copula of the bivariate distribution. λL plays an important role in modelling aggregate financial risk with copulas. This paper introduces three non-parametric estimators for λL. They are weakly consistent under mild regularity conditions on the copula and under the assumption that the number k = k(n) of observations in the lower tail, used for estimation, is asymptotically k ≈ √n. The finite sample properties of the estimators are investigated using a Monte Carlo simulation in special cases. It turns out that these estimators are biased, where amount and sign of the bias depend on the underlying copula, on the sample size n, on k, and on the true value of λL.

Suggested Citation

  • Jadran Dobric & Friedrich Schmid, 2005. "Nonparametric estimation of the lower tail dependence λL in bivariate copulas," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(4), pages 387-407.
  • Handle: RePEc:taf:japsta:v:32:y:2005:i:4:p:387-407
    DOI: 10.1080/02664760500079217
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760500079217
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/02664760500079217?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. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
    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. Dominique Guegan & Giovanni de Luca & Giorgia Rivieccio, 2017. "Three-stage estimation method for non-linear multiple time-series," Post-Print halshs-01439860, HAL.
    2. Peter Grundke, 2019. "Ranking consistency of systemic risk measures: a simulation-based analysis in a banking network model," Review of Quantitative Finance and Accounting, Springer, vol. 52(4), pages 953-990, May.
    3. Chen Yang & Wenjun Jiang & Jiang Wu & Xin Liu & Zhichuan Li, 2018. "Clustering of financial instruments using jump tail dependence coefficient," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 491-513, August.
    4. Fousekis, Panos & Grigoriadis, Vasilis, 2017. "Price co-movement and the crack spread in the US futures markets," Journal of Commodity Markets, Elsevier, vol. 7(C), pages 57-71.
    5. Li, Feng & Kang, Yanfei, 2018. "Improving forecasting performance using covariate-dependent copula models," International Journal of Forecasting, Elsevier, vol. 34(3), pages 456-476.
    6. Dominique Guegan & Giovanni de Luca & Giorgia Rivieccio, 2017. "Three-stage estimation method for non-linear multiple time-series," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01439860, HAL.
    7. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2017. "The kidnapping of Europe: High-order moments' transmission between developed and emerging markets," Emerging Markets Review, Elsevier, vol. 31(C), pages 96-115.
    8. Elena Di Bernardino & Didier Rullière, 2016. "On tail dependence coefficients of transformed multivariate Archimedean copulas," Post-Print hal-00992707, HAL.
    9. Yuri Salazar & Wing Ng, 2015. "Nonparametric estimation of general multivariate tail dependence and applications to financial time series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 121-158, March.
    10. Fousekis, Panos & Grigoriadis, Vasilis, 2016. "Spatial price dependence by time scale: Empirical evidence from the international butter markets," Economic Modelling, Elsevier, vol. 54(C), pages 195-204.
    11. Chen, Zhongfei & Wanke, Peter & Antunes, Jorge Junio Moreira & Zhang, Ning, 2017. "Chinese airline efficiency under CO2 emissions and flight delays: A stochastic network DEA model," Energy Economics, Elsevier, vol. 68(C), pages 89-108.
    12. Nikoloulopoulos, Aristidis K. & Joe, Harry & Li, Haijun, 2012. "Vine copulas with asymmetric tail dependence and applications to financial return data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3659-3673.
    13. Dominique Guegan & Giovanni De Luca & Giorgia Rivieccio, 2017. "Three-stage estimation method for non-linear multiple time-series," Documents de travail du Centre d'Economie de la Sorbonne 17001, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    14. Panagiotpu, Dimitrios & Stavrakoudis, Athanassios, 2021. "Price dependence among the major EU extra virgin olive oil markets: A time scale analysis," MPRA Paper 114656, University Library of Munich, Germany, revised Jun 2022.
    15. Luca, Giovanni De & Guégan, Dominique & Rivieccio, Giorgia, 2019. "Assessing tail risk for nonlinear dependence of MSCI sector indices: A copula three-stage approach," Finance Research Letters, Elsevier, vol. 30(C), pages 327-333.
    16. Fischer, Matthias J. & Hinzmann, Gerd, 2006. "A new class of copulas with tail dependence and a generalized tail dependence estimator," Discussion Papers 77/2006, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.

    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. Fathi, Abid & Nader, Naifar, 2007. "Price Calibration of basket default swap: Evidence from Japanese market," MPRA Paper 6013, University Library of Munich, Germany.
    2. Harris, Richard D.F. & Mazibas, Murat, 2013. "Dynamic hedge fund portfolio construction: A semi-parametric approach," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 139-149.
    3. Azam, Kazim & Pitt, Michael, 2014. "Bayesian Inference for a Semi-Parametric Copula-based Markov Chain," The Warwick Economics Research Paper Series (TWERPS) 1051, University of Warwick, Department of Economics.
    4. Fantazzini, Dean, 2010. "Three-stage semi-parametric estimation of T-copulas: Asymptotics, finite-sample properties and computational aspects," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2562-2579, November.
    5. Giacomini, Enzo & Härdle, Wolfgang & Spokoiny, Vladimir, 2009. "Inhomogeneous Dependence Modeling with Time-Varying Copulae," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 224-234.
    6. Param Silvapulle & Gunky Kim & Mervyn J. Silvapulle, 2004. "Robustness of a semiparametric estimator of a copula," Econometric Society 2004 Australasian Meetings 317, Econometric Society.
    7. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2006. "Vector Multiplicative Error Models: Representation and Inference," NBER Technical Working Papers 0331, National Bureau of Economic Research, Inc.
    8. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 22(2), pages 98-134.
    9. Yuri Salazar & Wing Ng, 2015. "Nonparametric estimation of general multivariate tail dependence and applications to financial time series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 121-158, March.
    10. Cooper, Joseph & Hungerford, Ashley & O'Donoghue, Erik, 2015. "Interactions of Shallow Loss Support and Traditional Federal Crop Insurance: Building a Framework for Assessing Commodity Support Issues for the Next Farm Act," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205310, Agricultural and Applied Economics Association.
    11. José Murteira & Óscar Lourenço, 2011. "Health care utilization and self-assessed health: specification of bivariate models using copulas," Empirical Economics, Springer, vol. 41(2), pages 447-472, October.
    12. MICHIELS, Frederik & DE SCHEPPER, Ann, 2007. "A copula test space model: How to avoid the wrong copula choice," Working Papers 2007027, University of Antwerp, Faculty of Business and Economics.
    13. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
    14. Zhichao Zhang & Li Ding & Fan Zhang & Zhuang Zhang, 2015. "Optimal Currency Composition for China's Foreign Reserves: A Copula Approach," The World Economy, Wiley Blackwell, vol. 38(12), pages 1947-1965, December.
    15. Domino, Krzysztof & Błachowicz, Tomasz, 2014. "The use of copula functions for modeling the risk of investment in shares traded on the Warsaw Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 77-85.
    16. Szego, Giorgio, 2005. "Measures of risk," European Journal of Operational Research, Elsevier, vol. 163(1), pages 5-19, May.
    17. Prokhorov, Artem & Schmidt, Peter, 2009. "Likelihood-based estimation in a panel setting: Robustness, redundancy and validity of copulas," Journal of Econometrics, Elsevier, vol. 153(1), pages 93-104, November.
    18. Yan, Jun, 2007. "Enjoy the Joy of Copulas: With a Package copula," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i04).
    19. Kole, H.J.W.G. & Koedijk, C.G. & Verbeek, M.J.C.M., 2003. "Stress Testing with Student's t Dependence," ERIM Report Series Research in Management ERS-2003-056-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    20. Vaz de Melo Mendes, Beatriz & Martins de Souza, Rafael, 2004. "Measuring financial risks with copulas," International Review of Financial Analysis, Elsevier, vol. 13(1), pages 27-45.

    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:taf:japsta:v:32:y:2005:i:4:p:387-407. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.