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Nonparametric drift estimation for diffusions with jumps driven by a Hawkes process

Author

Listed:
  • Charlotte Dion

    (Sorbonne Université, UMR CNRS 8001, LPSM)

  • Sarah Lemler

    (Université Paris-Saclay)

Abstract

We consider a 1-dimensional diffusion process X with jumps. The particularity of this model relies in the jumps which are driven by a multidimensional Hawkes process denoted N. This article is dedicated to the study of a nonparametric estimator of the drift coefficient of this original process. We construct estimators based on discrete observations of the process X in a high frequency framework with a large horizon time and on the observations of the process N. The proposed nonparametric estimator is built from a least squares contrast procedure on subspace spanned by trigonometric basis vectors. We obtain adaptive results that are comparable with the one obtained in the nonparametric regression context. We finally conduct a simulation study in which we first focus on the implementation of the process and then on showing the good behavior of the estimator.

Suggested Citation

  • Charlotte Dion & Sarah Lemler, 2020. "Nonparametric drift estimation for diffusions with jumps driven by a Hawkes process," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 489-515, October.
    • Handle: RePEc:spr:sistpr:v:23:y:2020:i:3:d:10.1007_s11203-020-09213-5
    DOI: 10.1007/s11203-020-09213-5
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    References listed on IDEAS

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