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Moments of the generalized hyperbolic distribution

Author

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  • Scott, David J
  • Würtz, Diethelm
  • Dong, Christine
  • Tran, Thanh Tam

Abstract

In this paper we demonstrate a recursive method for obtaining the moments of the generalized hyperbolic distribution. The method is readily programmable for numerical evaluation of moments. For low order moments we also give an alternative derivation of the moments of the generalized hyperbolic distribution. The expressions given for these moments may be used to obtain moments for special cases such as the hyperbolic and normal inverse Gaussian distributions. Moments for limiting cases such as the skew hyperbolic t and variance gamma distributions can be found using the same approach.

Suggested Citation

  • Scott, David J & Würtz, Diethelm & Dong, Christine & Tran, Thanh Tam, 2009. "Moments of the generalized hyperbolic distribution," MPRA Paper 19081, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:19081
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    References listed on IDEAS

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    Citations

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    Cited by:

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    2. Marco Bee & Maria Michela Dickson & Flavio Santi, 2018. "Likelihood-based risk estimation for variance-gamma models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 69-89, March.
    3. Paolella, Marc S. & Polak, Paweł, 2015. "COMFORT: A common market factor non-Gaussian returns model," Journal of Econometrics, Elsevier, vol. 187(2), pages 593-605.
    4. Matthias Wagener & Andriette Bekker & Mohammad Arashi, 2021. "Mastering the Body and Tail Shape of a Distribution," Mathematics, MDPI, vol. 9(21), pages 1-22, October.
    5. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.
    6. Arismendi, Juan C. & Broda, Simon, 2017. "Multivariate elliptical truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 29-44.
    7. Jose Luis Alayon G., 2015. "Distribucion hiperbolica generalizada: una aplicacion en la seleccion de portafolios y en cuantificacion de medidas de riesgo de mercado," Revista de Economía del Rosario, Universidad del Rosario, vol. 18(2), pages 249-308, December.
    8. Luo, Min & Kontosakos, Vasileios E. & Pantelous, Athanasios A. & Zhou, Jian, 2019. "Cryptocurrencies: Dust in the wind?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1063-1079.
    9. Zhang, Wenting & He, Xie & Hamori, Shigeyuki, 2023. "The impact of the COVID-19 pandemic and Russia-Ukraine war on multiscale spillovers in green finance markets: Evidence from lower and higher order moments," International Review of Financial Analysis, Elsevier, vol. 89(C).
    10. Trojan, Sebastian, 2013. "Regime Switching Stochastic Volatility with Skew, Fat Tails and Leverage using Returns and Realized Volatility Contemporaneously," Economics Working Paper Series 1341, University of St. Gallen, School of Economics and Political Science, revised Aug 2014.
    11. Ahmed BenSaïda & Sabri Boubaker & Duc Khuong Nguyen & Skander Slim, 2018. "Value‐at‐risk under market shifts through highly flexible models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 37(8), pages 790-804, December.

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    More about this item

    Keywords

    Generalized hyperbolic distribution; hyperbolic distribution; kurtosis; moments; normal inverse Gaussian distribution; skewed-t distribution; skewness; Student-t distribution.;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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