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

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.
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https://hal.archives-ouvertes.fr/hal-02094627
Contributor : Sarah Lemler <>
Submitted on : Monday, April 15, 2019 - 4:43:39 PM
Last modification on : Wednesday, May 15, 2019 - 4:12:06 AM

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  • HAL Id : hal-02094627, version 1
  • ARXIV : 1904.08232

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Charlotte Dion, Sarah Lemler. Nonparametric drift estimation for diffusions with jumps driven by a Hawkes process. 2019. ⟨hal-02094627⟩

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