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Multivariate elliptically contoured stable distributions: theory and estimation

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  • John Nolan

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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
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    File URL: http://hdl.handle.net/10.1007/s00180-013-0396-7
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    References listed on IDEAS

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    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.
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    Cited by:

    1. John P. Nolan, 2016. "An R package for modeling and simulating generalized spherical and related distributions," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-11, December.
    2. Meintanis, Simos G. & Ngatchou-Wandji, Joseph & Taufer, Emanuele, 2015. "Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 171-192.
    3. Barone, P., 2016. "Bivariate one-sample optimal location test for spherical stable densities by Pade’ methods," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 189-199.
    4. Dilip B. Madan, 2016. "Conic Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-42, May.
    5. repec:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-017-0544-4 is not listed on IDEAS

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