IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v135y2019icp56-69.html
   My bibliography  Save this article

A streaming algorithm for bivariate empirical copulas

Author

Listed:
  • Gregory, Alastair

Abstract

Empirical copula functions can be used to model the dependence structure of multivariate data. The Greenwald and Khanna algorithm is adapted in order to provide a space-memory efficient approximation to the empirical copula function of a bivariate stream of data. A succinct space-memory efficient summary of values seen in the stream up to a certain time is maintained and can be queried at any point to return an approximation to the empirical bivariate copula function with guaranteed error bounds. An example then illustrates how these summaries can be used as a tool to compute approximations to higher dimensional copula decompositions containing bivariate copulas. The computational benefits and approximation error of the algorithm are theoretically and numerically assessed.

Suggested Citation

  • Gregory, Alastair, 2019. "A streaming algorithm for bivariate empirical copulas," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 56-69.
    • Handle: RePEc:eee:csdana:v:135:y:2019:i:c:p:56-69
    DOI: 10.1016/j.csda.2019.01.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319300295
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2019.01.015?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. 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.
    2. Rafael Schmidt & Ulrich Stadtmüller, 2006. "Non‐parametric Estimation of Tail Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 307-335, June.
    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. Yanyuan Ma & Marc Genton & Emanuel Parzen, 2011. "Asymptotic properties of sample quantiles of discrete distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 227-243, April.
    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. Li, Feng & Kang, Yanfei, 2018. "Improving forecasting performance using covariate-dependent copula models," International Journal of Forecasting, Elsevier, vol. 34(3), pages 456-476.
    2. Li, Haijun & Wu, Peiling, 2013. "Extremal dependence of copulas: A tail density approach," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 99-111.
    3. Weiß, Gregor N.F. & Supper, Hendrik, 2013. "Forecasting liquidity-adjusted intraday Value-at-Risk with vine copulas," Journal of Banking & Finance, Elsevier, vol. 37(9), pages 3334-3350.
    4. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    5. Siburg, Karl Friedrich & Stoimenov, Pavel & Weiß, Gregor N.F., 2015. "Forecasting portfolio-Value-at-Risk with nonparametric lower tail dependence estimates," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 129-140.
    6. 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.
    7. Travkin, A., 2015. "Estimating Pair-Copula Constructions Using Empirical Tail Dependence Functions: an Application to Russian Stock Market," Journal of the New Economic Association, New Economic Association, vol. 25(1), pages 39-55.
    8. Kellner, Ralf & Rösch, Daniel, 2019. "A country specific point of view on international diversification," Journal of International Money and Finance, Elsevier, vol. 98(C), pages 1-1.
    9. Yuri Salazar Flores & Adán Díaz-Hernández, 2021. "Counterdiagonal/nonpositive tail dependence in Vine copula constructions: application to portfolio management," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 375-407, June.
    10. DAVID E. ALLEN & MICHAEL McALEER & ROBERT J. POWELL & ABHAY K. SINGH, 2018. "Non-Parametric Multiple Change Point Analysis Of The Global Financial Crisis," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 1-23, June.
    11. Rand Kwong Yew Low, 2018. "Vine copulas: modelling systemic risk and enhancing higher‐moment portfolio optimisation," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 58(S1), pages 423-463, November.
    12. Roger M. Cooke & Harry Joe & Bo Chang, 2020. "Vine copula regression for observational studies," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 141-167, June.
    13. Sleire, Anders D. & Støve, Bård & Otneim, Håkon & Berentsen, Geir Drage & Tjøstheim, Dag & Haugen, Sverre Hauso, 2022. "Portfolio allocation under asymmetric dependence in asset returns using local Gaussian correlations," Finance Research Letters, Elsevier, vol. 46(PB).
    14. Claudia Klüppelberg & Gabriel Kuhn & Liang Peng, 2008. "Semi‐Parametric Models for the Multivariate Tail Dependence Function – the Asymptotically Dependent Case," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 701-718, December.
    15. Zhang, Dalu, 2014. "Vine copulas and applications to the European Union sovereign debt analysis," International Review of Financial Analysis, Elsevier, vol. 36(C), pages 46-56.
    16. Portier, François & Segers, Johan, 2018. "On the weak convergence of the empirical conditional copula under a simplifying assumption," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 160-181.
    17. Victor Chernozhukov & Iván Fernández-Val & Blaise Melly & Kaspar Wüthrich, 2020. "Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 123-137, January.
    18. Reboredo, Juan C. & Ugolini, Andrea, 2015. "A vine-copula conditional value-at-risk approach to systemic sovereign debt risk for the financial sector," The North American Journal of Economics and Finance, Elsevier, vol. 32(C), pages 98-123.
    19. Sun, Fuqiang & Fu, Fangyou & Liao, Haitao & Xu, Dan, 2020. "Analysis of multivariate dependent accelerated degradation data using a random-effect general Wiener process and D-vine Copula," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    20. Zhichao Zhang & Fan Zhang & Zhuang Zhang, 2013. "Strategic Asset Allocation for China's Foreign Reserves: A Copula Approach," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 21(6), pages 1-21, 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:eee:csdana:v:135:y:2019:i:c:p:56-69. 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.