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

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  • Fischer, Matthias J.
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    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. --

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    Bibliographic Info

    Paper provided by Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics in its series Discussion Papers with number 46/2002.

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    Date of creation: 2002
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    Handle: RePEc:zbw:faucse:462002

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    Web page: http://www.statistik.wiso.uni-erlangen.de/
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    Related research

    Keywords: SGSH distribution; NEF-GHS distribution; skewness; GARCH; APARCH;

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    1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    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. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    4. Stefan Mittnik & Marc Paolella & Svetlozar Rachev, 1998. "Unconditional and Conditional Distributional Models for the Nikkei Index," Asia-Pacific Financial Markets, Springer, vol. 5(2), pages 99-128, May.
    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.
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