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Original Articles

On structure, family and parameter estimation of hierarchical Archimedean copulas

ORCID Icon, ORCID Icon & ORCID Icon
Pages 3261-3324 | Received 25 Oct 2016, Accepted 04 Aug 2017, Published online: 24 Aug 2017

References

  • Sklar A. Fonctions de répartition a n dimensions et leurs marges. Publ Inst Stat Univ Paris. 1959;8:229–231.
  • Nelsen R. An introduction to copulas. 2nd ed. New York: Springer-Verlag; 2006.
  • Joe H. Multivariate models and dependence concepts. London: Chapman & Hall; 1997.
  • Hofert M, Mächler M, McNeil AJ. Archimedean copulas in high dimensions: estimators and numerical challenges motivated by financial applications. Journal de la Société Française de Statistique. 2013;154(1):25–63.
  • Hofert M. Efficiently sampling nested Archimedean copulas. Comput Statist Data Anal. 2011;55(1):57–70. doi: 10.1016/j.csda.2010.04.025
  • Hofert M. A stochastic representation and sampling algorithm for nested Archimedean copulas. J Stat Comput Simul. 2012;82(9):1239–1255. doi: 10.1080/00949655.2011.574632
  • Okhrin O, Okhrin Y, Schmid W. On the structure and estimation of hierarchical Archimedean copulas. J Econometrics. 2013;173(2):189–204. Available from: http://www.sciencedirect.com/science/article/pii/S0304407612002667 doi: 10.1016/j.jeconom.2012.12.001
  • Górecki J, Holeňa M. Structure determination and estimation of hierarchical Archimedean copulas based on Kendall correlation matrix. In: Appice A, Ceci M, Loglisci C, et al., editors. New frontiers in mining complex patterns. Cham: Springer International Publishing; 2014. Lecture Notes in Computer Science; p. 132–147.
  • Górecki J, Hofert M, Holeňa M. On the consistency of an estimator for hierarchical Archimedean copulas. In: Talašová J, Stoklasa J, Talášek T, editors. 32nd international conference on mathematical methods in economics. Olomouc: Palacký University; 2014. p. 239–244.
  • Górecki J, Hofert M, Holeňa M. An approach to structure determination and estimation of hierarchical Archimedean copulas and its application to Bayesian classification. J Intell Inf Syst. 2016;46(1):21–59. doi: 10.1007/s10844-014-0350-3
  • Embrechts P, Hofert M, Wang R. Bernoulli and tail-dependence compatibility. Ann Appl Probab. 2016;26(3):1636–1658. Available from: http://dx.doi.org/10.1214/15-AAP1128 doi: 10.1214/15-AAP1128
  • Uyttendaele N. On the estimation of nested Archimedean copulas: a theoretical and an experimental comparison. Comput Statist. 2017. Available from: https://doi.org/10.1007/s00180-017-0743-1
  • McNeil AJ, Nešlehová J. Multivariate Archimedean copulas, d-monotone functions and l1-norm symmetric distributions. Ann Statist. 2009;37:3059–3097. doi: 10.1214/07-AOS556
  • Widder DV. The Laplace transform. Princeton: Princeton University Press; 1946.
  • Hofert M. Sampling nested Archimedean copulas with applications to cdo pricing. Suedwestdeutscher Verlag fuer Hochschulschriften; 2010. ISBN: 978-3-8381-1656-3
  • Hofert M, Scherer M. CDO pricing with nested Archimedean copulas. Quant Finance. 2011;11(5):775–787. doi: 10.1080/14697680903508479
  • Holeňa M, Ščavnický M. Application of copulas to data mining based on observational logic. In: ITAT 2013: Information technologies – applications and theory workshops, posters, and tutorials. Donovaly, Slovakia. North Charleston: CreateSpace Independent Publishing Platform; 2013. p. 77–85.
  • McNeil AJ. Sampling nested Archimedean copulas. J Stat Comput Simul. 2008;78(6):567–581. doi: 10.1080/00949650701255834
  • Holeňa M, Bajer L, Ščavnický M. Using copulas in data mining based on the observational calculus. IEEE Trans Knowl Data Eng. 2015;27(10):2851–2864. doi: 10.1109/TKDE.2015.2426705
  • Rezapour M. On the construction of nested Archimedean copulas for d-monotone generators. Statist Probab Lett. 2015;101:21–32. doi: 10.1016/j.spl.2015.03.001
  • Hofert M. Sampling Archimedean copulas. Comput Statist Data Anal. 2008;52(12):5163–5174. doi: 10.1016/j.csda.2008.05.019
  • Hering C, Hofert M, Mai JF, et al. Constructing hierarchical Archimedean copulas with Lèvy subordinators. J Multivariate Anal. 2010;101(6):1428–1433. Available from: http://www.sciencedirect.com/science/article/pii/S0047259X09001961 doi: 10.1016/j.jmva.2009.10.005
  • Genest C, Rivest LP. Statistical inference procedures for bivariate archimedean copulas. J Amer Statist Assoc. 1993;88(423):1034–1043. doi: 10.1080/01621459.1993.10476372
  • Cramér H. On the composition of elementary errors: first paper: mathematical deductions. Scand Actuar J. 1928;1928(1):13–74. doi: 10.1080/03461238.1928.10416862
  • Genest C, Rémillard B, Beaudoin D. Goodness-of-fit tests for copulas: a review and a power study. Insur Math Econ. 2009;44(2):199–213. doi: 10.1016/j.insmatheco.2007.10.005
  • Breiman L, Freidman J, Olshen R, et al. Classification and regression trees. Florida, US: Wadsworth; 1984.
  • Górecki J, Holeňa M. An alternative approach to the structure determination of hierarchical Archimedean copulas. Proceedings of the 31st international conference on mathematical methods in economics (MME 2013). Jihlava; 2013. p. 201–206.
  • Górecki J, Hofert M, Holeňa M. Kendall's tau and agglomerative clustering for structure determination of hierarchical archimedean copulas. Depend Model. 2017;5(1):75–87.
  • Clarke B, Fokoue E, Zhang HH. Principles and theory for data mining and machine learning. New York: Springer; 2009.
  • Batagelj V. Note on ultrametric hierarchical clustering algorithms. Psychometrika. 1981;46(3):351–352. Available from: http://dx.doi.org/10.1007/BF02293743 doi: 10.1007/BF02293743
  • Kojadinovic I, Yan J. Modeling multivariate distributions with continuous margins using the copula R package. J Statist Softw. 2010;34(9):1–20. doi: 10.18637/jss.v034.i09
  • Okhrin O, Ristig A. Hierarchical Archimedean copulae: the HAC package. J Statist Softw. 2014;58(4). 6. Available from: http://www.jstatsoft.org/v58/i04 doi: 10.18637/jss.v058.i04
  • Okhrin O, Ristig A, Sheen JR, et al. Conditional systemic risk with penalized copula [SFB 649 Discussion Paper 2015-038]. Berlin; 2015. Available from: http://hdl.handle.net/10419/121999
  • Segers J, Uyttendaele N. Nonparametric estimation of the tree structure of a nested Archimedean copula. Comput Statist Data Anal. 2014;72:190–204. doi: 10.1016/j.csda.2013.10.028
  • Górecki J, Hofert M, Holeňa M. Hierarchical Archimedean copulas for MATLAB and Octave: the HACopula toolbox. 2017. Available from: https://github.com/gorecki/HACopula
  • Okhrin O, Ristig A. Package ‘HAC’; 2015. Available from: ftp://journal.r-project.org/pub/R/web/packages/HAC/HAC.pdfftp://journal.r-project.org/pub/R/web/packages/HAC/HAC.pdf

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