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

  • Naoto Kunitomo

    (Faculty of Economics, The University of Tokyo)

  • Takashi Owada

    (Bank of Japan)

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    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.

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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2004/2004cf272.pdf
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    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-272.

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    Length: 30 pages
    Date of creation: Apr 2004
    Date of revision:
    Handle: RePEc:tky:fseres:2004cf272
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    1. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2001. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," CIRJE F-Series CIRJE-F-124, CIRJE, Faculty of Economics, University of Tokyo.
    2. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
    4. 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.
    5. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, October.
    6. Jian Zhang, 2003. "Sieve Empirical Likelihood and Extensions of the Generalized Least Squares," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 1-24.
    7. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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