Skew Generalized Secant Hyperbolic Distributions: Unconditional and Conditional Fit to Asset Returns
نویسنده
چکیده
A generalization of the hyperbolic secant distribution which allows for both skewness and 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 this class 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. Zusammenfassung: Eine Generalisierung der Secans hyperbolicus Verteilung, die sowohl Schiefe als auch Leptokurtosis erlaubt, ist in Morris (1982) angegeben. Unlängst wurde in Vaughan (2002) eine weitere flexible Verallgemeinerung vorgeschlagen, die zwar eine Reihe angenehmer Eigenschaften aufweist jedoch keine Schiefe erlaubt. Deshalb führten Fischer and Vaughan (2002) durch Aufteilung des Skalenparameters einen zusätzlichen Schiefeparameter ein und zeigten, dass die meisten angenehmen Eigenschaften dabei erhalten bleiben. Wir besprechen nochmals kurz diese Klasse von Verteilungen und wenden sie dann auf Ertragsdaten an. Bezüglich der Nikkei225 Daten wird gezeigt, dass diese Verteilungsklasse, die so genannte schiefe generalisierte Secans hyperbolicus Verteilung, bei bedingten und nicht-bedingten Ertragsmodellen eine ausgezeichnete Anpassung aufweist.
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