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Properties of hierarchical Archimedean copulas

Author

Listed:
  • Okhrin Ostap

    (Insitute for Statistics and Econometries, Humboldt Universität zu Berlin, Berlin, Deutschland)

  • Okhrin Yarema
  • Schmid Wolfgang

    (European University Viadrina, Department of Statistics, Frankfurt (Oder), Deutschland)

Abstract

In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean copulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula values, which is particularly useful for tests and constructing confidence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures, and extreme value copulas. We pay special attention to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas.

Suggested Citation

  • Okhrin Ostap & Okhrin Yarema & Schmid Wolfgang, 2013. "Properties of hierarchical Archimedean copulas," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 21-54, March.
    • Handle: RePEc:bpj:strimo:v:30:y:2013:i:1:p:21-54:n:2
    DOI: 10.1524/strm.2013.1071
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    References listed on IDEAS

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    Citations

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    Cited by:

    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. Ostap Okhrin & Martin Odening & Wei Xu, 2013. "Systemic Weather Risk and Crop Insurance: The Case of China," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(2), pages 351-372, June.
    3. Roland Strausz, 2009. "The Political Economy of Regulatory Risk," SFB 649 Discussion Papers SFB649DP2009-040, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Göran Kauermann & Christian Schellhase & David Ruppert, 2013. "Flexible Copula Density Estimation with Penalized Hierarchical B-splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 685-705, December.
    5. Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2016. "Goodness-of-fit test for specification of semiparametric copula dependence models," Journal of Econometrics, Elsevier, vol. 193(1), pages 215-233.
    6. Zolotko, Mikhail & Okhrin, Ostap, 2014. "Modelling the general dependence between commodity forward curves," Energy Economics, Elsevier, vol. 43(C), pages 284-296.
    7. 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.
    8. Benjamin Poignard & Jean-David Fermanian, 2019. "The finite sample properties of Sparse M-estimators with Pseudo-Observations," Working Papers 2019-01, Center for Research in Economics and Statistics.
    9. Penikas, H., 2010. "Financial Applications of Copula-Models," Journal of the New Economic Association, New Economic Association, issue 7, pages 24-44.
    10. Michał Grajek & Lars-Hendrik Röller, 2012. "Regulation and Investment in Network Industries: Evidence from European Telecoms," Journal of Law and Economics, University of Chicago Press, vol. 55(1), pages 189-216.
    11. Awondo, Sebastain N. & Shurley, Don W., 2017. "On the Efficiency of Pseudo Risk Pools and Proxy Yield Data on Crop Insurance and Reinsurance in U.S," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258566, Agricultural and Applied Economics Association.
    12. Nikolaus Hautsch & Julia Schuamburg & Melanie Schienle, 2012. "Modeling Time-Varying Dependencies between Positive-Valued High-Frequency Time Series," SFB 649 Discussion Papers SFB649DP2012-054, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Barbara Choroś & Wolfgang Härdle & Ostap Okhrin, 2009. "CDO and HAC," SFB 649 Discussion Papers SFB649DP2009-038, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Göran Kauermann & Renate Meyer, 2014. "Penalized marginal likelihood estimation of finite mixtures of Archimedean copulas," Computational Statistics, Springer, vol. 29(1), pages 283-306, February.
    15. Maria Grith & Wolfgang Härdle & Juhyun Park, 2009. "Shape invariant modelling pricing kernels and risk aversion," SFB 649 Discussion Papers SFB649DP2009-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Henry Penikas, 2016. "Copula-Based Univariate Time Series Structural Shift Identification Test," Papers 1609.05056, arXiv.org.
    17. Ostap Okhrin, 2010. "Fitting high-dimensional Copulae to Data," SFB 649 Discussion Papers SFB649DP2010-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    18. Zhou, Rui & Ji, Min, 2021. "Modelling mortality dependence: An application of dynamic vine copula," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 241-255.
    19. Choroś-Tomczyk, Barbara & Härdle, Wolfgang Karl & Okhrin, Ostap, 2013. "Valuation of collateralized debt obligations with hierarchical Archimedean copulae," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 42-62.
    20. Osama Ahmed & Teresa Serra, 2015. "Economic analysis of the introduction of agricultural revenue insurance contracts in Spain using statistical copulas," Agricultural Economics, International Association of Agricultural Economists, vol. 46(1), pages 69-79, January.
    21. Aepli, Matthias D. & Frauendorfer, Karl & Fuess, Roland & Paraschiv, Florentina, 2015. "Multivariate Dynamic Copula Models: Parameter Estimation and Forecast Evaluation," Working Papers on Finance 1513, University of St. Gallen, School of Finance.

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    More about this item

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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