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On estimating the tail index and the spectral measure of multivariate \(\alpha \)-stable distributions

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Abstract

We propose estimators for the tail index and the spectral measure of multivariate \(\alpha \)-stable distributions and derive their asymptotic properties. Simulation studies reveal the appropriateness of the estimators. Applications to financial data are also considered.

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Acknowledgments

The authors would like to thank an anonymous reviewer and Editor, Professor Norbert Henze, for their valuable comments and suggestions to improve the manuscript. They are also grateful to Professor John P. Nolan to provide access to STABLE package in R for improving the computations and Dr. Thaigo do Rego Sousa for his help in running the programs of GEVStableGarch package. The third author was supported by JSPS KAKENHI Grant Number 26870655.

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Author notes

  1. Adel Mohammadpour

    Present address: Department of Economics, McGill University, Montréal, Canada

Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran, Iran

    Mohammad Mohammadi & Adel Mohammadpour

  2. School of Business Administration, Faculty of Urban Liberal Arts, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo, Japan

    Hiroaki Ogata

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  1. Mohammad Mohammadi
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  2. Adel Mohammadpour
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  3. Hiroaki Ogata
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Correspondence to Adel Mohammadpour.

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Mohammadi, M., Mohammadpour, A. & Ogata, H. On estimating the tail index and the spectral measure of multivariate \(\alpha \)-stable distributions. Metrika 78, 549–561 (2015). https://doi.org/10.1007/s00184-014-0515-7

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  • DOI: https://doi.org/10.1007/s00184-014-0515-7

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