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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. 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.
    2. 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).
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    1. 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.
    2. De Keyser, Steven & Gijbels, Irène, 2024. "Parametric dependence between random vectors via copula-based divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    3. Sydney Benson & Regina Burroughs & Vladimir Ladyzhets & Jessica Mohr & Arkady Shemyakin & David Walczak & Huan Zhang, 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.
    4. 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).
    5. Ostap Okhrin & Anastasija Tetereva, 2017. "The Realized Hierarchical Archimedean Copula in Risk Modelling," Econometrics, MDPI, vol. 5(2), pages 1-31, June.
    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. Shahid Latif & Slobodan P. Simonovic, 2023. "Trivariate Probabilistic Assessments of the Compound Flooding Events Using the 3-D Fully Nested Archimedean (FNA) Copula in the Semiparametric Distribution Setting," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(4), pages 1641-1693, March.
    8. 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.
    9. 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).
    10. 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.
    11. 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.
    12. 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.
    13. 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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    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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