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On the Estimation of Skewed Geometric Stable Distributions

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Abstract

The increasing interest in the application of geometric stable distributions has lead to a need for appropriate estimators. Building on recent procedures for estimating the Linnik distribution, this paper develops two estimators for the geometric stable distribution. Closed form expressions are provided for the signed and unsigned fractional moments of the distribution. The estimators are then derived using the methods of fractional lower order moments and that of logarithmic moments. Their performance is tested on simulated data, where the lower order estimators, in particular, are found to give efficient results over most of the parameter space.

Suggested Citation

  • Halvarsson, Daniel, 2013. "On the Estimation of Skewed Geometric Stable Distributions," Ratio Working Papers 216, The Ratio Institute.
    • Handle: RePEc:hhs:ratioi:0216
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    References listed on IDEAS

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    1. Manas, Arnaud, 2012. "The Laplace illusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3963-3970.
    2. Devroye, Luc, 1990. "A note on linnik's distribution," Statistics & Probability Letters, Elsevier, vol. 9(4), pages 305-306, April.
    3. V. Lekshmi & K. Jose, 2004. "An autoregressive process with geometric α-laplace marginals," Statistical Papers, Springer, vol. 45(3), pages 337-350, July.
    4. Anderson, Dale N., 1992. "A multivariate Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 333-336, July.
    5. repec:nys:sunysb:93-02 is not listed on IDEAS
    6. Kotz, Samuel & Ostrovskii, I. V., 1996. "A mixture representation of the Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 61-64, January.
    7. Dexter Cahoy, 2012. "An estimation procedure for the Linnik distribution," Statistical Papers, Springer, vol. 53(3), pages 617-628, August.
    8. Pakes, Anthony G., 1998. "Mixture representations for symmetric generalized Linnik laws," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 213-221, March.
    9. Kozubowski, Tomasz J. & Rachev, Svetlozar T., 1994. "The theory of geometric stable distributions and its use in modeling financial data," European Journal of Operational Research, Elsevier, vol. 74(2), pages 310-324, April.
    10. Jose, K.K. & Tomy, Lishamol & Sreekumar, J., 2008. "Autoregressive processes with normal-Laplace marginals," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2456-2462, October.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Geometric stable distribution; Estimation; Fractional lower order moments; Logarithmic moments; Economics;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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