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Nonparametric adaptive estimation of linear functionals for low frequency observed Lévy processes

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  • Kappus, Johanna

Abstract

For a Lévy process X having finite variation on compact sets and finite first moments, u (dx) = xv (dx) is a finite signed measure which completely describes the jump dynamics. We construct kernel estimators for linear functionals of u and provide rates of convergence under regularity assumptions. Moreover, we consider adaptive estimation via model selection and propose a new strategy for the data driven choice of the smoothing parameter.

Suggested Citation

  • Kappus, Johanna, 2012. "Nonparametric adaptive estimation of linear functionals for low frequency observed Lévy processes," SFB 649 Discussion Papers 2012-016, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2012-016
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    References listed on IDEAS

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    1. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    2. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    3. repec:hum:wpaper:sfb649dp2006-034 is not listed on IDEAS
    4. Shota Gugushvili, 2009. "Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(3), pages 321-343.
    5. repec:hum:wpaper:sfb649dp2006-035 is not listed on IDEAS
    6. 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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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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