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

Charlotte Dion () and Sarah Lemler
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Charlotte Dion: Sorbonne Université, UMR CNRS 8001, LPSM
Sarah Lemler: Université Paris-Saclay

Statistical Inference for Stochastic Processes, 2020, vol. 23, issue 3, No 2, 489-515

Abstract: 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.

Keywords: Nonparametric estimator; Model selection; Diffusion; Hawkes process (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11203-020-09213-5

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