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Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables

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  • Fuchs, Sebastian
  • Di Lascio, F. Marta L.
  • Durante, Fabrizio

Abstract

A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that are comonotonic. Various properties of this dissimilarity are studied, with special attention to those that are prone to the hierarchical agglomerative methods, such as reducibility. Some insights are provided for the use of such a measure in clustering algorithms and a simulation study is presented. Real case studies illustrate the main features of the whole methodology.

Suggested Citation

  • Fuchs, Sebastian & Di Lascio, F. Marta L. & Durante, Fabrizio, 2021. "Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:csdana:v:159:y:2021:i:c:s0167947321000359
    DOI: 10.1016/j.csda.2021.107201
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    1. Matthieu Marbac & Christophe Biernacki & Vincent Vandewalle, 2017. "Model-based clustering of Gaussian copulas for mixed data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(23), pages 11635-11656, December.
    2. Paul Embrechts & Marius Hofert, 2013. "A note on generalized inverses," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 423-432, June.
    3. Giovanni De Luca & Paola Zuccolotto, 2017. "Dynamic tail dependence clustering of financial time series," Statistical Papers, Springer, vol. 58(3), pages 641-657, September.
    4. Marco Scarsini, 1984. "Strong measures of concordance and convergence in probability," Post-Print hal-00542387, HAL.
    5. Chen Yang & Wenjun Jiang & Jiang Wu & Xin Liu & Zhichuan Li, 2018. "Clustering of financial instruments using jump tail dependence coefficient," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 491-513, August.
    6. Durante Fabrizio & Puccetti Giovanni & Scherer Matthias & Vanduffel Steven, 2016. "Distributions with given marginals: the beginnings: An interview with Giorgio Dall’Aglio," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-14, November.
    7. Jae Youn Ahn & Sebastian Fuchs, 2020. "On Minimal Copulas under the Concordance Order," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 762-780, March.
    8. Müller, Alfred & Scarsini, Marco, 2000. "Some Remarks on the Supermodular Order," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 107-119, April.
    9. F. Marta L. Lascio & Simone Giannerini, 2019. "Clustering dependent observations with copula functions," Statistical Papers, Springer, vol. 60(1), pages 35-51, February.
    10. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
    11. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate conditional versions of Spearman's rho and related measures of tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1123-1140, July.
    12. Sunil Kumar & Nivedita Deo, 2012. "Correlation, Network and Multifractal Analysis of Global Financial Indices," Papers 1202.0409, arXiv.org.
    13. Giovanni De Luca & Paola Zuccolotto, 2011. "A tail dependence-based dissimilarity measure for financial time series clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 323-340, December.
    14. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    15. De Luca Giovanni & Zuccolotto Paola, 2017. "A double clustering algorithm for financial time series based on extreme events," Statistics & Risk Modeling, De Gruyter, vol. 34(1-2), pages 1-12, June.
    16. G. Bonanno & G. Caldarelli & F. Lillo & S. Micciché & N. Vandewalle & R. Mantegna, 2004. "Networks of equities in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 38(2), pages 363-371, March.
    17. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    18. Manuel Úbeda-Flores, 2005. "Multivariate versions of Blomqvist’s beta and Spearman’s footrule," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 781-788, December.
    19. Dißmann, J. & Brechmann, E.C. & Czado, C. & Kurowicka, D., 2013. "Selecting and estimating regular vine copulae and application to financial returns," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 52-69.
    20. Perreault, Samuel & Duchesne, Thierry & Nešlehová, Johanna G., 2019. "Detection of block-exchangeable structure in large-scale correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 400-422.
    21. Fabrizio Durante & Roberta Pappadà & Nicola Torelli, 2014. "Clustering of financial time series in risky scenarios," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(4), pages 359-376, December.
    22. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    23. Kojadinovic, Ivan, 2010. "Hierarchical clustering of continuous variables based on the empirical copula process and permutation linkages," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 90-108, January.
    24. Gijbels, Irène & Kika, Vojtěch & Omelka, Marek, 2021. "On the specification of multivariate association measures and their behaviour with increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    25. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    26. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    27. Hao Ji & Hao Wang & Brunero Liseo, 2018. "Portfolio Diversification Strategy Via Tail‐Dependence Clustering and ARMA‐GARCH Vine Copula Approach," Australian Economic Papers, Wiley Blackwell, vol. 57(3), pages 265-283, September.
    28. Fabrizio Durante & Roberta Pappadà & Nicola Torelli, 2015. "Clustering of time series via non-parametric tail dependence estimation," Statistical Papers, Springer, vol. 56(3), pages 701-721, August.
    29. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    30. Taylor M. D., 2016. "Multivariate measures of concordance for copulas and their marginals," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-13, October.
    31. Krupskii, Pavel & Joe, Harry, 2020. "Flexible copula models with dynamic dependence and application to financial data," Econometrics and Statistics, Elsevier, vol. 16(C), pages 148-167.
    32. Acar, Elif F. & Czado, Claudia & Lysy, Martin, 2019. "Flexible dynamic vine copula models for multivariate time series data," Econometrics and Statistics, Elsevier, vol. 12(C), pages 181-197.
    33. Kojadinovic, Ivan, 2004. "Agglomerative hierarchical clustering of continuous variables based on mutual information," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 269-294, June.
    34. Grothe, Oliver & Schnieders, Julius & Segers, Johan, 2014. "Measuring association and dependence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 96-110.
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