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Skew generalized secant hyperbolic distributions: unconditional and conditional fit to asset returns

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  • Fischer, Matthias J.

Abstract

A generalization of the hyperbolic secant distribution which allows both for skewness and for leptokurtosis was given by Morris (1982). Recently, Vaughan (2002) proposed another flexible generalization of the hyperbolic secant distribution which has a lot of nice properties but is not able to allow for skewness. For this reason, Fischer and Vaughan (2002) additionally introduced a skewness parameter by means of splitting the scale parameter and showed that most of the nice properties are preserved. We briefly review both classes of distributions and apply them to financial return data. By means of the Nikkei225 data, it will be shown that this class of distributions - the socalled skew generalized secant hyperbolic distribution - provides an excellent fit in the context of unconditional and conditional return models.

Suggested Citation

  • Fischer, Matthias J., 2002. "Skew generalized secant hyperbolic distributions: unconditional and conditional fit to asset returns," Discussion Papers 46/2002, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    • Handle: RePEc:zbw:faucse:462002
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    References listed on IDEAS

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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. McDonald, James B., 1991. "Parametric models for partially adaptive estimation with skewed and leptokurtic residuals," Economics Letters, Elsevier, vol. 37(3), pages 273-278, November.
    3. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    4. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    5. Fischer, Matthias J., 2002. "Solving the Esscher puzzle: the NEF-GHS option pricing model," Discussion Papers 42a/2002, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    6. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    7. Stefan Mittnik & Marc Paolella & Svetlozar Rachev, 1998. "Unconditional and Conditional Distributional Models for the Nikkei Index," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 5(2), pages 99-128, May.
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    Cited by:

    1. Palmitesta Paola & Provasi Corrado, 2004. "GARCH-type Models with Generalized Secant Hyperbolic Innovations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-19, May.

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    More about this item

    Keywords

    SGSH distribution; NEF-GHS distribution; skewness; GARCH; APARCH;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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