IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v203y2024ics0047259x24000435.html
   My bibliography  Save this article

Parametric dependence between random vectors via copula-based divergence measures

Author

Listed:
  • De Keyser, Steven
  • Gijbels, Irène

Abstract

This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of Φ-divergences. An axiomatic framework for this purpose is provided, after which we focus on the absolutely continuous setting assuming copula densities exist. We consider parametric and semi-parametric frameworks, discuss estimation procedures, and report on asymptotic properties of the proposed estimators. In particular, we first concentrate on a Gaussian copula approach yielding explicit and attractive dependence coefficients for specific choices of Φ, which are more amenable for estimation. Next, general parametric copula families are considered, with special attention to nested Archimedean copulas, being a natural choice for dependence modelling of random vectors. The results are illustrated by means of examples. Simulations and a real-world application on financial data are provided as well.

Suggested Citation

  • De Keyser, Steven & Gijbels, Irène, 2024. "Parametric dependence between random vectors via copula-based divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:jmvana:v:203:y:2024:i:c:s0047259x24000435
    DOI: 10.1016/j.jmva.2024.105336
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X24000435
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2024.105336?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hofert, Marius & Pham, David, 2013. "Densities of nested Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 37-52.
    2. Okhrin, Ostap & Ristig, Alexander, 2014. "Hierarchical Archimedean Copulae: The HAC Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i04).
    3. Xudong Wang & Xiaofeng Hui, 2017. "Mutual Information Based Analysis for the Distribution of Financial Contagion in Stock Markets," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-13, October.
    4. Gallegati, Marco, 2012. "A wavelet-based approach to test for financial market contagion," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3491-3497.
    5. Ferdinand Österreicher & Igor Vajda, 2003. "A new class of metric divergences on probability spaces and its applicability in statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 639-653, September.
    6. Gery Geenens & Pierre Lafaye de Micheaux, 2022. "The Hellinger Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 639-653, April.
    7. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate extensions of Spearman's rho and related statistics," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 407-416, February.
    8. Gaißer, Sandra & Ruppert, Martin & Schmid, Friedrich, 2010. "A multivariate version of Hoeffding's Phi-Square," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2571-2586, November.
    9. Akhtaruzzaman, Md & Boubaker, Sabri & Sensoy, Ahmet, 2021. "Financial contagion during COVID–19 crisis," Finance Research Letters, Elsevier, vol. 38(C).
    10. Mordant, Gilles & Segers, Johan, 2022. "Measuring dependence between random vectors via optimal transport," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    11. Wu, Edmond H.C. & Yu, Philip L.H. & Li, W.K., 2009. "A smoothed bootstrap test for independence based on mutual information," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2524-2536, May.
    12. Harry Joe, 1989. "Estimation of entropy and other functionals of a multivariate density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(4), pages 683-697, December.
    13. 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).
    14. Hofert, Marius & Oldford, Wayne & Prasad, Avinash & Zhu, Mu, 2019. "A framework for measuring association of random vectors via collapsed random variables," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 5-27.
    15. Ivan Medovikov & Artem Prokhorov, 2017. "A New Measure of Vector Dependence, with Applications to Financial Risk and Contagion," Journal of Financial Econometrics, Oxford University Press, vol. 15(3), pages 474-503.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mordant, Gilles & Segers, Johan, 2022. "Measuring dependence between random vectors via optimal transport," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Liebscher Eckhard, 2014. "Copula-based dependence measures," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-16, October.
    3. 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.
    4. Choi, Sun-Yong, 2022. "Credit risk interdependence in global financial markets: Evidence from three regions using multiple and partial wavelet approaches," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 80(C).
    5. García, Jesús E. & González-López, V.A. & Nelsen, R.B., 2013. "A new index to measure positive dependence in trivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 481-495.
    6. Fan, Yanqin & Henry, Marc, 2023. "Vector copulas," Journal of Econometrics, Elsevier, vol. 234(1), pages 128-150.
    7. Lingyue Zhang & Dawei Lu & Xiaoguang Wang, 2020. "Measuring and testing interdependence among random vectors based on Spearman’s $$\rho $$ ρ and Kendall’s $$\tau $$ τ," Computational Statistics, Springer, vol. 35(4), pages 1685-1713, December.
    8. Gaißer, Sandra & Ruppert, Martin & Schmid, Friedrich, 2010. "A multivariate version of Hoeffding's Phi-Square," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2571-2586, November.
    9. Yanqin Fan & Marc Henry, 2020. "Vector copulas," Papers 2009.06558, arXiv.org, revised Apr 2021.
    10. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2022. "Stochastic representation of FGM copulas using multivariate Bernoulli random variables," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    11. 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).
    12. Shahzad, Syed Jawad Hussain & Nor, Safwan Mohd & Kumar, Ronald Ravinesh & Mensi, Walid, 2017. "Interdependence and contagion among industry-level US credit markets: An application of wavelet and VMD based copula approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 310-324.
    13. Okhrin, Ostap & Ristig, Alexander, 2014. "Hierarchical Archimedean Copulae: The HAC Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i04).
    14. Saba Qureshi & Muhammad Aftab, 2023. "Exchange Rate Interdependence in ASEAN Markets: A Wavelet Analysis," Global Business Review, International Management Institute, vol. 24(6), pages 1180-1204, December.
    15. Marcos Albuquerque Junior & José António Filipe & Paulo de Melo Jorge Neto & Cristiano da Costa da Silva, 2021. "Assessing the Time-Frequency Co-Movements among the Five Largest Engineering Consulting Companies: A Wavelet-Base Metrics of Contagion and VaR Ratio," Mathematics, MDPI, vol. 9(5), pages 1-16, March.
    16. Zhou, Zhongbao & Lin, Ling & Li, Shuxian, 2018. "International stock market contagion: A CEEMDAN wavelet analysis," Economic Modelling, Elsevier, vol. 72(C), pages 333-352.
    17. Bhuiyan, Rubaiyat Ahsan & Husain, Afzol & Zhang, Changyong, 2021. "A wavelet approach for causal relationship between bitcoin and conventional asset classes," Resources Policy, Elsevier, vol. 71(C).
    18. Serdar Neslihanoglu, 2021. "Linearity extensions of the market model: a case of the top 10 cryptocurrency prices during the pre-COVID-19 and COVID-19 periods," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-27, December.
    19. Liebscher Eckhard, 2017. "Copula-Based Dependence Measures For Piecewise Monotonicity," Dependence Modeling, De Gruyter, vol. 5(1), pages 198-220, August.
    20. Alqahtani, Faisal & Hamdi, Besma & Hammoudeh, Shawkat, 2021. "The effects of global factors on the Saudi Arabia equity market by firm size: Implications for risk management based on quantile analysis and frequency domain causality," Journal of Multinational Financial Management, Elsevier, vol. 61(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:203:y:2024:i:c:s0047259x24000435. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.