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On the local asymptotic behavior of the likelihood function for Meixner Lévy processes under high-frequency sampling

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  • Kawai, Reiichiro
  • Masuda, Hiroki

Abstract

We discuss the local asymptotic behavior of the likelihood function associated with all the four characterizing parameters ([alpha],[beta],[delta],[mu]) of the Meixner Lévy process under high-frequency sampling scheme. We derive the optimal rate of convergence for each parameter and the Fisher information matrix in a closed form. The skewness parameter [beta] exhibits a slower rate alone, relative to the other three parameters free of sampling rate. An unusual aspect is that the Fisher information matrix is constantly singular for full joint estimation of the four parameters. This is a particular phenomenon in the regular high-frequency sampling setting and is of essentially different nature from low-frequency sampling. As soon as either [alpha] or [delta] is fixed, the Fisher information matrix becomes diagonal, implying that the corresponding maximum likelihood estimators are asymptotically orthogonal.

Suggested Citation

  • Kawai, Reiichiro & Masuda, Hiroki, 2011. "On the local asymptotic behavior of the likelihood function for Meixner Lévy processes under high-frequency sampling," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 460-469, April.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:4:p:460-469
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    References listed on IDEAS

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    1. Yacine Aït-Sahalia & Jean Jacod, 2008. "Fisher's Information for Discretely Sampled Lévy Processes," Econometrica, Econometric Society, vol. 76(4), pages 727-761, July.
    2. Hiroki Masuda, 2009. "Notes on estimating inverse-Gaussian and gamma subordinators under high-frequency sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 181-195, March.
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    Cited by:

    1. Clément, Emmanuelle & Gloter, Arnaud, 2015. "Local Asymptotic Mixed Normality property for discretely observed stochastic differential equations driven by stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2316-2352.

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