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

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  • Johanna Kappus
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    Abstract

    For a Lévy process X having finite variation on compact sets and finite first moments, µ( dx) = xv( dx) is a finite signed measure which completely describes the jump dynamics. We construct kernel estimators for linear functionals of µ 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.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2012-016.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2012-016.

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    Length: 39 pages
    Date of creation: Feb 2012
    Date of revision:
    Handle: RePEc:hum:wpaper:sfb649dp2012-016

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    Related research

    Keywords: Statistics of stochastic processes; Low frequency observed Lévy processes; Nonparametric statistics; Adaptive estimation; Model selection with unknown variance;

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    References

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    1. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA.
    2. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy Models [1]," SFB 649 Discussion Papers SFB649DP2006-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Geman, Hélyette & Carr, Peter & Madan, Dilip B. & Yor, Marc, 2003. "Stochastic Volatility for Levy Processes," Open Access publications from Université Paris-Dauphine urn:hdl:123456789/1392, Université Paris-Dauphine.
    4. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy Models [2]," SFB 649 Discussion Papers SFB649DP2006-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Figueroa-López, José E., 2008. "Small-time moment asymptotics for Lévy processes," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3355-3365, December.
    6. F. Comte & C. Lacour, 2011. "Data‐driven density estimation in the presence of additive noise with unknown distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 601-627, 09.
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