IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v118y2013icp37-52.html
   My bibliography  Save this article

Densities of nested Archimedean copulas

Author

Listed:
  • Hofert, Marius
  • Pham, David

Abstract

Nested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean copulas. However, for likelihood based inference it is important to have the density. The present work fills this gap. A general formula for the derivatives of the nodes and inner generators appearing in nested Archimedean copulas is developed. This leads to a tractable formula for the density of nested Archimedean copulas in arbitrary dimensions if the number of nesting levels is not too large. Various examples including famous Archimedean families and transformations of such are given. Furthermore, a numerically efficient way to evaluate the log-density is presented.

Suggested Citation

  • Hofert, Marius & Pham, David, 2013. "Densities of nested Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 37-52.
    • Handle: RePEc:eee:jmvana:v:118:y:2013:i:c:p:37-52
    DOI: 10.1016/j.jmva.2013.03.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1300033X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.03.006?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. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    2. Hofert, Marius & Maechler, Martin, 2011. "Nested Archimedean Copulas Meet R: The nacopula Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i09).
    3. Hofert, Marius, 2011. "Efficiently sampling nested Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 57-70, January.
    4. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. De Keyser, Steven & Gijbels, Irène, 2024. "Parametric dependence between random vectors via copula-based divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    2. Rezapour, Mohsen, 2015. "On the construction of nested Archimedean copulas for d-monotone generators," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 21-32.
    3. Benjamin Poignard & Jean-David Fermanian, 2022. "The finite sample properties of sparse M-estimators with pseudo-observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 1-31, February.
    4. Vettori, Sabrina & Huser, Raphael & Segers, Johan & Genton, Marc, 2017. "Bayesian Clustering and Dimension Reduction in Multivariate Extremes," LIDAM Discussion Papers ISBA 2017017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. De Backer, Mickael & El Ghouch, Anouar & Van Keilegom, Ingrid, 2016. "Semiparametric Copula Quantile Regression for Complete or Censored Data," LIDAM Discussion Papers ISBA 2016009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Fatima Palacios‐Rodriguez & Elena Di Bernardino & Melina Mailhot, 2023. "Smooth copula‐based generalized extreme value model and spatial interpolation for extreme rainfall in Central Eastern Canada," Environmetrics, John Wiley & Sons, Ltd., vol. 34(3), May.
    7. Mirza Nazmul Hasan & Roel Braekers, 2021. "Estimation of the association parameters in hierarchically clustered survival data by nested Archimedean copula functions," Computational Statistics, Springer, vol. 36(4), pages 2755-2787, December.
    8. Elena Di Bernardino & Didier Rullière, 2015. "Estimation of multivariate critical layers: Applications to rainfall data," Post-Print hal-00940089, HAL.
    9. Mazo, Gildas & Uyttendaele, Nathan, 2016. "Building conditionally dependent parametric one-factor copulas," LIDAM Discussion Papers ISBA 2016004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1(2013), pages 1-36, October.
    11. 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.
    12. 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.
    13. 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.
    14. Mai Jan-Frederik, 2019. "Simulation algorithms for hierarchical Archimedean copulas beyond the completely monotone case," Dependence Modeling, De Gruyter, vol. 7(1), pages 202-214, January.
    15. Nabil Kazi-Tani & Didier Rullière, 2019. "On a construction of multivariate distributions given some multidimensional marginals," Post-Print hal-01575169, HAL.
    16. Grothe, Oliver & Hofert, Marius, 2015. "Construction and sampling of Archimedean and nested Archimedean Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 182-198.

    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. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
    2. Bedoui, Rihab & Braiek, Sana & Guesmi, Khaled & Chevallier, Julien, 2019. "On the conditional dependence structure between oil, gold and USD exchange rates: Nested copula based GJR-GARCH model," Energy Economics, Elsevier, vol. 80(C), pages 876-889.
    3. Okhrin, Ostap & Ristig, Alexander, 2014. "Hierarchical Archimedean Copulae: The HAC Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i04).
    4. Jörg Schwiebert, 2016. "Multinomial choice models based on Archimedean copulas," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 333-354, July.
    5. Hofert, Marius & Vrins, Frédéric, 2013. "Sibuya copulas," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 318-337.
    6. Eckhard Liebscher, 2024. "Fitting copulas in the case of missing data," Statistical Papers, Springer, vol. 65(6), pages 3681-3711, August.
    7. Chaoubi, Ihsan & Cossette, Hélène & Marceau, Etienne & Robert, Christian Y., 2021. "Hierarchical copulas with Archimedean blocks and asymmetric between-block pairs," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    8. repec:hum:wpaper:sfb649dp2012-036 is not listed on IDEAS
    9. 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.
    10. Górecki, Jan & Hofert, Marius & Okhrin, Ostap, 2021. "Outer power transformations of hierarchical Archimedean copulas: Construction, sampling and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    11. Diers, Dorothea & Eling, Martin & Marek, Sebastian D., 2012. "Dependence modeling in non-life insurance using the Bernstein copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 430-436.
    12. 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.
    13. Bedoui, Rihab & Braeik, Sana & Goutte, Stéphane & Guesmi, Khaled, 2018. "On the study of conditional dependence structure between oil, gold and USD exchange rates," International Review of Financial Analysis, Elsevier, vol. 59(C), pages 134-146.
    14. Zhang, Kong-Sheng & Lin, Jin-Guan & Xu, Pei-Rong, 2016. "A new class of copulas involving geometric distribution: Estimation and applications," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 1-10.
    15. Cossette, Hélène & Marceau, Etienne & Mtalai, Itre & Veilleux, Déry, 2018. "Dependent risk models with Archimedean copulas: A computational strategy based on common mixtures and applications," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 53-71.
    16. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    17. Paul Embrechts & Marius Hofert, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 263-270, August.
    18. Li, Heping & Zhu, Wenjin & Dieulle, Laurence & Deloux, Estelle, 2022. "Condition-based maintenance strategies for stochastically dependent systems using Nested Lévy copulas," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    19. 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).
    20. Stanislav Anatolyev & Vladimir Pyrlik, 2021. "Shrinkage for Gaussian and t Copulas in Ultra-High Dimensions," CERGE-EI Working Papers wp699, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    21. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1(2013), pages 1-36, October.

    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:118:y:2013:i:c:p:37-52. 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.