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Indirect estimation of elliptical stable distributions

Author

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  • LOMBARDI, Marco
  • VEREDAS, David

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Abstract

We present an indirect estimation approach for elliptical stable distributions which relies on the use of a multivariate t distribution as auxiliary model. This distribution is also elliptical and we show that its parameters have a one-to-one relationship with those of the elliptical stable, therefore making the proposed indirect approach especially suitable.Standard asymptotic properties are also shown and we analyze the finite sample behavior of the estimators via a comprehensive Monte Carlo study. An application to 27 emerging markets stock indexes concludes the paper.

Suggested Citation

  • LOMBARDI, Marco & VEREDAS, David, 2007. "Indirect estimation of elliptical stable distributions," LIDAM Discussion Papers CORE 2007018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2007018
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    Cited by:

    1. Ogata, Hiroaki, 2013. "Estimation for multivariate stable distributions with generalized empirical likelihood," Journal of Econometrics, Elsevier, vol. 172(2), pages 248-254.
    2. Matteo Barigozzi & Roxana Halbleib & David Veredas, 2012. "Which model to match?," Working Papers 1229, Banco de España.
    3. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    4. Calzolari, Giorgio & Halbleib, Roxana & Parrini, Alessandro, 2014. "Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 158-171.
    5. Lambert, Philippe & Laurent, Sébastien & Veredas, David, 2012. "Testing conditional asymmetry: A residual-based approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1229-1247.
    6. Sladana Babic & Laetitia Gelbgras & Marc Hallin & Christophe Ley, 2019. "Optimal tests for elliptical symmetry: specified and unspecified location," Working Papers ECARES 2019-26, ULB -- Universite Libre de Bruxelles.
    7. Tsionas, Mike G., 2016. "Bayesian analysis of multivariate stable distributions using one-dimensional projections," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 185-193.
    8. Matteo Bonato, 2012. "Modeling fat tails in stock returns: a multivariate stable-GARCH approach," Computational Statistics, Springer, vol. 27(3), pages 499-521, September.
    9. Simos G. Meintanis & John P. Nolan & Charl Pretorius, 2024. "Specification procedures for multivariate stable-Paretian laws for independent and for conditionally heteroskedastic data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(2), pages 517-539, June.
    10. 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.
    11. Alexeev, Vitali & Maynard, Alex, 2012. "Localized level crossing random walk test robust to the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3322-3344.
    12. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
    13. Calzolari, Giorgio & Halbleib, Roxana, 2018. "Estimating stable latent factor models by indirect inference," Journal of Econometrics, Elsevier, vol. 205(1), pages 280-301.
    14. Stolfi, Paola & Bernardi, Mauro & Petrella, Lea, 2025. "Sparse simulation-based estimator built on quantiles," Econometrics and Statistics, Elsevier, vol. 34(C), pages 32-43.
    15. Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, vol. 4(2), pages 1-28, May.
    16. Paola Stolfi & Mauro Bernardi & Lea Petrella, 2016. "Multivariate Method Of Simulated Quantiles," Departmental Working Papers of Economics - University 'Roma Tre' 0212, Department of Economics - University Roma Tre.
    17. 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.
    18. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.
    19. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.

    More about this item

    Keywords

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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