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Article Dans Une Revue Statistical Inference for Stochastic Processes Année : 2020

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

Résumé

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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Dates et versions

hal-02094627 , version 1 (15-04-2019)
hal-02094627 , version 2 (24-10-2019)

Identifiants

Citer

Charlotte Dion, Sarah Lemler. Nonparametric drift estimation for diffusions with jumps driven by a Hawkes process. Statistical Inference for Stochastic Processes, 2020, ⟨10.1007/s11203-020-09213-5⟩. ⟨hal-02094627v2⟩
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