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Indirect estimation of elliptical stable distributions


  • LOMBARDI, Marco
  • VEREDAS, David



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," CORE Discussion Papers 2007018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2007018

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    References listed on IDEAS

    1. B. N. Cheng & S. T. Rachev, 1995. "Multivariate Stable Futures Prices," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 133-153.
    2. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 63-84, Suppl. De.
    3. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    4. Frahm, Gabriel & Junker, Markus & Szimayer, Alexander, 2003. "Elliptical copulas: applicability and limitations," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 275-286, July.
    5. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2002. "Stationarity of stable power-GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 97-107, January.
    6. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
    7. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    8. Luc Bauwens & Sébastien Laurent, 2002. "A New Class of Multivariate skew Densities, with Application to GARCH Models," Computing in Economics and Finance 2002 5, Society for Computational Economics.
    9. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    10. Garcia, René & Renault, Eric & Veredas, David, 2011. "Estimation of stable distributions by indirect inference," Journal of Econometrics, Elsevier, vol. 161(2), pages 325-337, April.
    11. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.
    12. Ghose, Devajyoti & Kroner, Kenneth F., 1995. "The relationship between GARCH and symmetric stable processes: Finding the source of fat tails in financial data," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 225-251, September.
    13. 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.
    14. Marco J. Lombardi & Giorgio Calzolari, 2008. "Indirect Estimation of α-Stable Distributions and Processes," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 193-208, March.
    15. J. Huston McCulloch, 2003. "The Risk-Neutral Measure and Option Pricing under Log-Stable Uncertainty," Working Papers 03-07, Ohio State University, Department of Economics.
    16. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," Review of Economic Studies, Oxford University Press, vol. 71(4), pages 945-973.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. repec:gam:jecnmx:v:4:y:2016:i:2:p:25:d:69492 is not listed on IDEAS
    6. 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.
    7. 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.
    8. Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-28, May.
    9. 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.
    10. Ogata, Hiroaki, 2013. "Estimation for multivariate stable distributions with generalized empirical likelihood," Journal of Econometrics, Elsevier, vol. 172(2), pages 248-254.
    11. Matteo Barigozzi & Roxana Halbleib & David Veredas, "undated". "Which model to match?," ULB Institutional Repository 2013/136240, ULB -- Universite Libre de Bruxelles.
    12. Giorgio Calzolari & Roxana Halbleib, 2014. "Estimating Stable Factor Models By Indirect Inference," Working Paper Series of the Department of Economics, University of Konstanz 2014-25, Department of Economics, University of Konstanz.
    13. Matteo Bonato, 2012. "Modeling fat tails in stock returns: a multivariate stable-GARCH approach," Computational Statistics, Springer, vol. 27(3), pages 499-521, September.
    14. 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.
    15. 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


    stable; elliptical; high dimension; multivariate; indirect inference;

    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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