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Efficient estimation of stable Lévy process with symmetric jumps

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  • Alexandre Brouste

    (Le Mans Université Avenue Olivier Messiaen)

  • Hiroki Masuda

    (Kyushu University)

Abstract

Efficient estimation of a non-Gaussian stable Lévy process with drift and symmetric jumps observed at high frequency is considered. For this statistical experiment, the local asymptotic normality of the likelihood is proved with a non-singular Fisher information matrix through the use of a non-diagonal norming matrix. The asymptotic normality and efficiency of a sequence of roots of the associated likelihood equation are shown as well. Moreover, we show that a simple preliminary method of moments can be used as an initial estimator of a scoring procedure, thereby conveniently enabling us to bypass numerically demanding likelihood optimization. Our simulation results show that the one-step estimator can exhibit quite similar finite-sample performance as the maximum likelihood estimator.

Suggested Citation

  • Alexandre Brouste & Hiroki Masuda, 2018. "Efficient estimation of stable Lévy process with symmetric jumps," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 289-307, July.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:2:d:10.1007_s11203-018-9181-0
    DOI: 10.1007/s11203-018-9181-0
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    References listed on IDEAS

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    1. Todorov, Viktor, 2013. "Power variation from second order differences for pure jump semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2829-2850.
    2. Yacine Aït-Sahalia & Jean Jacod, 2008. "Fisher's Information for Discretely Sampled Lévy Processes," Econometrica, Econometric Society, vol. 76(4), pages 727-761, July.
    3. Hiroki Masuda, 2010. "On Statistical Aspects in Calibrating a Geometric Skewed Stable Asset Price Model," World Scientific Book Chapters, in: Masaaki Kijima & Chiaki Hara & Keiichi Tanaka & Yukio Muromachi (ed.), Recent Advances In Financial Engineering 2009, chapter 7, pages 181-202, World Scientific Publishing Co. Pte. Ltd..
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