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Moments of the generalized hyperbolic distribution

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  • David Scott
  • Diethelm Würtz
  • Christine Dong
  • Thanh Tran

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.
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  • David Scott & Diethelm Würtz & Christine Dong & Thanh Tran, 2011. "Moments of the generalized hyperbolic distribution," Computational Statistics, Springer, vol. 26(3), pages 459-476, September.
    • Handle: RePEc:spr:compst:v:26:y:2011:i:3:p:459-476
    DOI: 10.1007/s00180-010-0219-z
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    Cited by:

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    2. Arismendi, Juan C. & Broda, Simon, 2017. "Multivariate elliptical truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 29-44.
    3. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.
    4. 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.
    5. Xiao Jiang & Saralees Nadarajah & Thomas Hitchen, 2024. "A Review of Generalized Hyperbolic Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 595-624, July.
    6. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    7. 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).
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.

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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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