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On estimating the tail index and the spectral measure of multivariate $$\alpha $$ α -stable distributions

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  • Mohammad Mohammadi
  • Adel Mohammadpour
  • Hiroaki Ogata

Abstract

We propose estimators for the tail index and the spectral measure of multivariate $$\alpha $$ α -stable distributions and derive their asymptotic properties. Simulation studies reveal the appropriateness of the estimators. Applications to financial data are also considered. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Mohammad Mohammadi & Adel Mohammadpour & Hiroaki Ogata, 2015. "On estimating the tail index and the spectral measure of multivariate $$\alpha $$ α -stable distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 549-561, July.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:5:p:549-561
    DOI: 10.1007/s00184-014-0515-7
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    References listed on IDEAS

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    1. Ogata, Hiroaki, 2013. "Estimation for multivariate stable distributions with generalized empirical likelihood," Journal of Econometrics, Elsevier, vol. 172(2), pages 248-254.
    2. repec:ulb:ulbeco:2013/136280 is not listed on IDEAS
    3. 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.
    4. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.
    5. Pivato, Marcus & Seco, Luis, 2003. "Estimating the spectral measure of a multivariate stable distribution via spherical harmonic analysis," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 219-240, November.
    6. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.
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    Cited by:

    1. 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).

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