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Hierarchical Archimedean copulae: The HAC package

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  • Okhrin, Ostap
  • Ristig, Alexander

Abstract

This paper aims at explanation of the R-package HAC, which provides user friendly methods for dealing with high-dimensional hierarchical Archimedean copulae (HAC). A computationally effcient estimation procedure allows to recover the structure and the parameters of HACs from data. In addition, arbitrary HACs can be constructed to sample random vectors and to compute the values of the corresponding cumulative distribution as well as density functions. Accurate graphics of the important characteristics of the package's object hac can be produced by the generic plot function.

Suggested Citation

  • Okhrin, Ostap & Ristig, Alexander, 2012. "Hierarchical Archimedean copulae: The HAC package," SFB 649 Discussion Papers 2012-036, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2012-036
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    References listed on IDEAS

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    1. Okhrin, Ostap & Ristig, Alexander, 2014. "Hierarchical Archimedean Copulae: The HAC Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i04).
    2. 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.
    3. 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.
    4. Hofert, Marius & Maechler, Martin, 2011. "Nested Archimedean Copulas Meet R: The nacopula Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i09).
    5. Okhrin, Ostap & Okhrin, Yarema & Schmid, Wolfgang, 2009. "Properties of hierarchical Archimedean copulas," SFB 649 Discussion Papers 2009-014, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Kojadinovic, Ivan & Yan, Jun, 2010. "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i09).
    7. Cornelia Savu & Mark Trede, 2010. "Hierarchies of Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 295-304.
    8. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
    9. Okhrin Ostap & Okhrin Yarema & Schmid Wolfgang, 2013. "Properties of hierarchical Archimedean copulas," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 21-54, March.
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    Cited by:

    1. Okhrin, Ostap & Ristig, Alexander & Sheen, Jeffrey R. & Trück, Stefan, 2015. "Conditional systemic risk with penalized copula," SFB 649 Discussion Papers 2015-038, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. Tente, Natalia & von Westernhagen, Natalja & Slopek, Ulf, 2017. "M-PRESS-CreditRisk: A holistic micro- and macroprudential approach to capital requirements," Discussion Papers 15/2017, Deutsche Bundesbank.
    3. Uyttendaele, Nathan, 2016. "On the estimation of nested Archimedean copulas: A theoretical and an experimental comparison," LIDAM Discussion Papers ISBA 2016005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Okhrin, Ostap & Ristig, Alexander, 2012. "Hierarchical Archimedean copulae: The HAC package," SFB 649 Discussion Papers 2012-036, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. repec:hum:wpaper:sfb649dp2015-038 is not listed on IDEAS
    6. Nathan Uyttendaele, 2018. "On the estimation of nested Archimedean copulas: a theoretical and an experimental comparison," Computational Statistics, Springer, vol. 33(2), pages 1047-1070, June.
    7. Martin Waltz & Abhay Kumar Singh & Ostap Okhrin, 2022. "Vulnerability-CoVaR: investigating the crypto-market," Quantitative Finance, Taylor & Francis Journals, vol. 22(9), pages 1731-1745, September.
    8. Penikas, Henry, 2014. "Investment portfolio risk modelling based on hierarchical copulas," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 35(3), pages 18-38.
    9. Benson, Sydney & Burroughs, Regina & Ladyzhets, Vladimir & Mohr, Jessica & Shemyakin, Arkady & Walczak, David & Zhang, Huan, 2020. "Copula models of economic capital for life insurance companies," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 32-54.
    10. ARAUJO ENCISO Sergio Rene & PIERALLI SIMONE & PEREZ DOMINGUEZ Ignacio, 2017. "Partial Stochastic Analysis with the Aglink-Cosimo Model: A Methodological Overview," JRC Research Reports JRC108837, Joint Research Centre.
    11. Ostap Okhrin & Anastasija Tetereva, 2017. "The Realized Hierarchical Archimedean Copula in Risk Modelling," Econometrics, MDPI, vol. 5(2), pages 1-31, June.
    12. Antonov I. N. & Knyazev A. G. & Lepekhin O. A., 2016. "Copula Models of the Joint Distribution of Exchange Rates," World of economics and management / Vestnik NSU. Series: Social and Economics Sciences, Socionet, vol. 16(4), pages 20-38.
    13. Segers, Johan & Uyttendaele, Nathan, 2013. "Nonparametric estimation of the tree structure of a nested Archimedean copula," LIDAM Discussion Papers ISBA 2013009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Feng, Xiaoguang & Hayes, Dermot, 2014. "Is Government Involvement Really Necessary: Implications for Systemic Risk and Crop Reinsurance Contracts," 2014 AAEA: Crop Insurance and the 2014 Farm Bill Symposium: Implementing Change in U.S. Agricultural Policy, October 8-9, 2014, Louisville, KY 184241, Agricultural and Applied Economics Association.
    15. Okhrin, Ostap & Ristig, Alexander, 2014. "Hierarchical Archimedean Copulae: The HAC Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i04).
    16. Segers, Johan & Uyttendaele, Nathan, 2014. "Nonparametric estimation of the tree structure of a nested Archimedean copula," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 190-204.
    17. Jakob Kevin & Fischer Matthias, 2014. "Quantifying the impact of different copulas in a generalized CreditRisk+ framework An empirical study," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-21.
    18. Seyyed Ali Zeytoon Nejad Moosavian & Barry K. Goodwin, 2021. "Flexible modelling of multivariate risks in pricing margin protection insurance: modelling portfolio risks with mixtures of mixtures," Applied Economics, Taylor & Francis Journals, vol. 53(4), pages 411-440, January.
    19. Nuño Martinez, Edgar & Cutululis, Nicolaos & Sørensen, Poul, 2018. "High dimensional dependence in power systems: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 94(C), pages 197-213.
    20. Pawlak, Jacek & Polak, John W. & Sivakumar, Aruna, 2017. "A framework for joint modelling of activity choice, duration, and productivity while travelling," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 153-172.
    21. Natalia Tente & Natalja Von Westernhagen & Ulf Slopek, 2019. "M‐PRESS‐CreditRisk: Microprudential and Macroprudential Capital Requirements for Credit Risk under Systemic Stress," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 51(7), pages 1923-1961, October.
    22. Targino, Rodrigo S. & Peters, Gareth W. & Shevchenko, Pavel V., 2015. "Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 206-226.
    23. Okhrin, Ostap & Xu, Ya Fei, 2017. "A comparison study of pricing credit default swap index tranches with convex combination of copulae," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 193-217.

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    More about this item

    Keywords

    copula; R; hierarchical Archimedean copula (HAC);
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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