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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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