IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v28y2013i5p2067-2089.html
   My bibliography  Save this article

Multivariate elliptically contoured stable distributions: theory and estimation

Author

Listed:
  • John Nolan

Abstract

Stable distributions with elliptical contours are a class of distributions that are useful for modeling heavy tailed multivariate data. This paper describes the theory of such distributions, presents formulas for calculating their densities, and methods for fitting the data and assessing the fit. Efficient numerical routines are implemented and evaluated in simulations. Applications to data sets of a financial portfolio with 30 assets and to a bivariate radar clutter data set are presented. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • John Nolan, 2013. "Multivariate elliptically contoured stable distributions: theory and estimation," Computational Statistics, Springer, vol. 28(5), pages 2067-2089, October.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:5:p:2067-2089
    DOI: 10.1007/s00180-013-0396-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-013-0396-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-013-0396-7?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. Byczkowski, T. & Nolan, J. P. & Rajput, B., 1993. "Approximation of Multidimensional Stable Densities," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 13-31, July.
    2. Marco Lombardi & David Veredas, 2009. "Indirect inference of elliptical fat tailed distributions," ULB Institutional Repository 2013/136204, ULB -- Universite Libre de Bruxelles.
    3. Abdul-Hamid, Husein & Nolan, John P., 1998. "Multivariate Stable Densities as Functions of One Dimensional Projections," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 80-89, October.
    4. Rafael Schmidt, 2002. "Tail dependence for elliptically contoured distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 301-327, May.
    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. Szabolcs Majoros & Andr'as Zempl'eni, 2018. "Multivariate stable distributions and their applications for modelling cryptocurrency-returns," Papers 1810.09521, arXiv.org.
    2. Paola Stolfi & Mauro Bernardi & Lea Petrella, 2018. "The sparse method of simulated quantiles: An application to portfolio optimization," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 375-398, August.
    3. Matsui, Muneya & Takemura, Akimichi, 2009. "Integral representations of one-dimensional projections for multivariate stable densities," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 334-344, March.
    4. Karling, Maicon J. & Lopes, Sílvia R.C. & de Souza, Roberto M., 2023. "Multivariate α-stable distributions: VAR(1) processes, measures of dependence and their estimations," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    5. Joe, Harry & Li, Haijun & Nikoloulopoulos, Aristidis K., 2010. "Tail dependence functions and vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 252-270, January.
    6. Abdul-Hamid, Husein & Nolan, John P., 1998. "Multivariate Stable Densities as Functions of One Dimensional Projections," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 80-89, October.
    7. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2016. "Copula--based Specification of vector MEMs," Papers 1604.01338, arXiv.org.
    8. Nolan, John P., 2018. "Truncated fractional moments of stable laws," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 312-318.
    9. Melanie Frick, 2012. "Measures of multivariate asymptotic dependence and their relation to spectral expansions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(6), pages 819-831, August.
    10. Chen, Ray-Bing & Guo, Meihui & Härdle, Wolfgang Karl & Huang, Shih-Feng, 2008. "Independent component analysis via copula techniques," SFB 649 Discussion Papers 2008-004, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    11. Mendes, Beatriz V.M. & Leal, Ricardo P.C. & Carvalhal-da-Silva, Andre, 2007. "Clustering in emerging equity markets," Emerging Markets Review, Elsevier, vol. 8(3), pages 194-205, September.
    12. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodri­guez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2008. "On the construction of copulas and quasi-copulas with given diagonal sections," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 473-483, April.
    13. Kexin Li & Jianxu Liu & Yuting Xue & Sanzidur Rahman & Songsak Sriboonchitta, 2022. "Consequences of Ignoring Dependent Error Components and Heterogeneity in a Stochastic Frontier Model: An Application to Rice Producers in Northern Thailand," Agriculture, MDPI, vol. 12(8), pages 1-17, July.
    14. Ghosh, Santu & Ayyala, Deepak Nag & Hellebuyck, Rafael, 2021. "Two-sample high dimensional mean test based on prepivots," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    15. Joe, Harry & Li, Haijun, 2019. "Tail densities of skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 421-435.
    16. Battey, Heather & Linton, Oliver, 2014. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 43-67.
    17. Takaaki Koike & Marius Hofert, 2020. "Modality for Scenario Analysis and Maximum Likelihood Allocation," Papers 2005.02950, arXiv.org, revised Nov 2020.
    18. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2017. "Copula–Based vMEM Specifications versus Alternatives: The Case of Trading Activity," Econometrics, MDPI, vol. 5(2), pages 1-24, April.
    19. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 22(2), pages 98-134.
    20. Jianhua Lin & Xiaohu Li, 2014. "Multivariate Generalized Marshall–Olkin Distributions and Copulas," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 53-78, March.

    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:spr:compst:v:28:y:2013:i:5:p:2067-2089. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.