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Estimation of the characteristics of a Lévy process observed at arbitrary frequency

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  • Johanna Kappus
  • Markus Reiß

Abstract

A Lévy process is observed at time points of distance Δ until time T. We construct an estimator of the Lévy–Khinchine characteristics of the process and derive optimal rates of convergence simultaneously in T and Δ. Thereby, we encompass the usual low‐ and high‐frequency assumptions and also obtain asymptotics in the mid‐frequency regime.

Suggested Citation

  • Johanna Kappus & Markus Reiß, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(3), pages 314-328, August.
    • Handle: RePEc:bla:stanee:v:64:y:2010:i:3:p:314-328
    DOI: 10.1111/j.1467-9574.2010.00461.x
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    Cited by:

    1. Kato, Kengo & Kurisu, Daisuke, 2020. "Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1159-1205.
    2. Trabs, Mathias, 2011. "Calibration of self-decomposable Lévy models," SFB 649 Discussion Papers 2011-073, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

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