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The Cumulant Generating Function Estimation Method

Author

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  • Knight, John L.
  • Satchell, Stephen E.

Abstract

This paper deals with the use of the empirical cumulant generating function to consistently estimate the parameters of a distribution from data that are independent and identically distributed (i.i.d.). The technique is particularly suited to situations where the density function is unknown or unbounded in parameter space. We prove asymptotic equivalence of our technique to that of the empirical characteristic function and outline a six-step procedure for its implementation. Extensions of the approach to non-i.i.d. situations are considered along with a discussion of suitable applications and a worked example.

Suggested Citation

  • Knight, John L. & Satchell, Stephen E., 1997. "The Cumulant Generating Function Estimation Method," Econometric Theory, Cambridge University Press, vol. 13(2), pages 170-184, April.
    • Handle: RePEc:cup:etheor:v:13:y:1997:i:02:p:170-184_00
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    Cited by:

    1. Chihwa Kao & Yongmiao Hong, 2004. "Detecting Neglected Nonlinearity in Dynamic Panel Data with Time-Varying Conditional Heteroskedasticity," Econometric Society 2004 Far Eastern Meetings 753, Econometric Society.
    2. Emanuele Taufer, 2008. "Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes," DISA Working Papers 0805, Department of Computer and Management Sciences, University of Trento, Italy, revised 07 Jul 2008.
    3. repec:oup:rapstu:v:7:y:2017:i:1:p:2-42. is not listed on IDEAS
    4. Kangrong Tan & Meifen Chu, 2012. "Estimation Of Portfolio Return And Value At Risk Using A Class Of Gaussian Mixture Distributions," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 6(1), pages 97-107.
    5. Annika Krutto, 2016. "Parameter Estimation in Stable Law," Risks, MDPI, vol. 4(4), pages 1-15, November.
    6. Michael Rockinger & Maria Semenova, 2005. "Estimation of Jump-Diffusion Process vis Empirical Characteristic Function," FAME Research Paper Series rp150, International Center for Financial Asset Management and Engineering.
    7. Maria P. Braun & Simos G. Meintanis & Viatcheslav B. Melas, 2008. "Optimal Design Approach to GMM Estimation of Parameters Based on Empirical Transforms," International Statistical Review, International Statistical Institute, vol. 76(3), pages 387-400, December.
    8. Stojanović, Vladica S. & Popović, Biljana Č. & Milovanović, Gradimir V., 2016. "The Split-SV model," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 560-581.
    9. Steven L. Heston & Alberto G. Rossi, 2017. "A Spanning Series Approach to Options," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 7(1), pages 2-42.

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