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An EM type algorithm for maximum likelihood estimation of the normal-inverse Gaussian distribution

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  • Karlis, Dimitris

Abstract

The Normal-Inverse Gaussian distribution arises as a Normal variance-mean mixture with an Inverse Gaussian mixing distribution. This article deals with Maximum Likelihood estimation of the parameters of the Normal-Inverse Gaussian distribution. Due to the complexity of the likelihood, direct maximization is difficult. An EM type algorithm is provided for the Maximum Likelihood estimation of the Normal-Inverse Gaussian distribution. This algorithm overcomes numerical difficulties occurring when standard numerical techniques are used. An application to a data set concerning the general index of the Athens Stock Exchange is given. Some operating characteristics of the algorithm are discussed.

Suggested Citation

  • Karlis, Dimitris, 2002. "An EM type algorithm for maximum likelihood estimation of the normal-inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 43-52, March.
  • Handle: RePEc:eee:stapro:v:57:y:2002:i:1:p:43-52
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    References listed on IDEAS

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    1. Vrontos, I D & Dellaportas, P & Politis, D N, 2000. "Full Bayesian Inference for GARCH and EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 187-198, April.
    2. Ole E. Barndorff-Nielsen & Karsten Prause, 2001. "Apparent scaling," Finance and Stochastics, Springer, vol. 5(1), pages 103-113.
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    Cited by:

    1. Zakamouline, Valeri & Koekebakker, Steen, 2009. "Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1242-1254, July.
    2. Zhao, Kaifeng & Lian, Heng, 2016. "The Expectation–Maximization approach for Bayesian quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 1-11.
    3. Yang Minxian, 2011. "Volatility Feedback and Risk Premium in GARCH Models with Generalized Hyperbolic Distributions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(3), pages 1-21, May.
    4. Olivia Andreea Baciu, 2015. "Generalized Hyperbolic Distributions: Empirical Evidence on Bucharest Stock Exchange," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 7(1), pages 007-018, June.
    5. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
    6. repec:eee:csdana:v:115:y:2017:i:c:p:136-154 is not listed on IDEAS
    7. repec:spr:annopr:v:255:y:2017:i:1:d:10.1007_s10479-015-1967-5 is not listed on IDEAS
    8. 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.
    9. Stefano Iacus & Lorenzo Mercuri, 2015. "Implementation of Lévy CARMA model in Yuima package," Computational Statistics, Springer, vol. 30(4), pages 1111-1141, December.
    10. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0601.
    11. Loregian, Angela & Mercuri, Lorenzo & Rroji, Edit, 2012. "Approximation of the variance gamma model with a finite mixture of normals," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 217-224.
    12. Wraith, Darren & Forbes, Florence, 2015. "Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 61-73.

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