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GARCH-type Models with Generalized Secant Hyperbolic Innovations

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  • Palmitesta Paola

    (University of Siena, Italy)

  • Provasi Corrado

    (University of Padua)

Abstract

GARCH-type models have been analyzed assuming various nongaussian distributions of errors. In general, the asymmetric generalized Student-t random variable seems to be the distribution which better captures the nonnormality features of financial data. However, a drawback of this distribution is represented by the technical dificulties due to the evaluation of moments, especially in the case of fractional degrees of freedom. In this paper we propose to model high frequency time series returns using GARCH-type models with a generalized secant hyperbolic (GSH) distribution. The main advantage of the GSH distribution over the Student-t distribution is that all the moments are finite for each value of the shape parameter. The distribution is symmetric with respect to the mean, but we show that it is still possible to obtain the density in a closed form introducing a skewness parameter according to the method proposed by Fernandez and Steel. We use a Monte Carlo experiment to validate this distribution in the context of GARCH models with maximum likelihood estimates of parameters. Finally, we show an application to log returns of a stock index.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:sndecm:v:8:y:2004:i:2:n:7
    DOI: 10.2202/1558-3708.1212
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    References listed on IDEAS

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    Cited by:

    1. Ahmed Shamiri & Abu Hassan, 2005. "Modeling and Forecasting Volatility of the Malaysian and the Singaporean stock indices using Asymmetric GARCH models and Non-normal Densities," Econometrics 0509015, University Library of Munich, Germany.
    2. Paola Palmitesta & Corrado Provasi, 2005. "Aggregation of Dependent Risks Using the Koehler–Symanowski Copula Function," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 189-205, February.
    3. Paola Palmitesta & Corrado Provasi, 2004. "Aggregation of Dependent Risks with Specific Marginals by the Family of Koehler-Symanowski Distributions," Computing in Economics and Finance 2004 306, Society for Computational Economics.
    4. Luca Bagnato & Valerio Potì & Maria Zoia, 2015. "The role of orthogonal polynomials in adjusting hyperpolic secant and logistic distributions to analyse financial asset returns," Statistical Papers, Springer, vol. 56(4), pages 1205-1234, November.

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