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

Author

Listed:
  • Johanna Kappus

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.

Suggested Citation

  • Johanna Kappus, 2012. "Nonparametric adaptive estimation of linear functionals for low frequency observed Lévy processes," SFB 649 Discussion Papers SFB649DP2012-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2012-016
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2012-016.pdf
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    3. Figueroa-López, José E., 2008. "Small-time moment asymptotics for Lévy processes," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3355-3365, December.
    4. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    5. 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, September.
    6. repec:taf:gnstxx:v:21:y:2009:i:3:p:321-343 is not listed on IDEAS
    7. repec:dau:papers:123456789/1392 is not listed on IDEAS
    8. Helyette Geman & P. Carr & D. Madan & M. Yor, 2003. "Stochastic Volatility for Levy Processes," Post-Print halshs-00144385, HAL.
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    Cited by:

    1. Mélina Bec & Claire Lacour, 2015. "Adaptive pointwise estimation for pure jump Lévy processes," Statistical Inference for Stochastic Processes, Springer, vol. 18(3), pages 229-256, October.

    More about this item

    Keywords

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

    JEL classification:

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

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