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Empirical Likelihood Estimation of Levy Processes (Revised: March 2005)

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  • Naoto Kunitomo

    (Faculty of Economics, The University of Tokyo)

  • Takashi Owada

    (Bank of Japan)

Abstract

We propose a new parameter estimation procedure for the Levy processes and the class of infinitely divisible distribution. We shall show that the empirical likelihood method gives an easy way to estimate the key parameters of the infinitely divisible distributions including the class of stable distributions as a special case. The maximum empirical likelihood estimator by using the empirical characteristic functions gives the consistency, the asymptotic normality, and the asymptotic efficiency for the key parameters when the number of restrictions on the empirical characteristic functions is large. Test procedures can be also developed. Some extensions to the estimating equations problem with the infinitely divisible distributions are discussed.

Suggested Citation

  • Naoto Kunitomo & Takashi Owada, 2004. "Empirical Likelihood Estimation of Levy Processes (Revised: March 2005)," CIRJE F-Series CIRJE-F-272, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2004cf272
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    References listed on IDEAS

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    6. Naoto Kunitomo & Yukitoshi Matsushita, 2003. "On Finite Sample Distributions of the Empirical Likelihood Estimator and the GMM Estimator," CIRJE F-Series CIRJE-F-200, CIRJE, Faculty of Economics, University of Tokyo.
    7. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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