Volume 22, 2018
|Page(s)||236 - 260|
|Published online||25 January 2019|
Adaptive nonparametric drift estimation of an integrated jump diffusion process
TU Dortmund, Faculty of Mathematics,
Dortmund, Germany .
2 Université Lille 1, Laboratoire Paul Painlevé, 59655 Villeneuve d’Ascq, France .
* Corresponding author: firstname.lastname@example.org
Accepted: 16 January 2018
In the present article, we investigate nonparametric estimation of the unknown drift function b in an integrated Lévy driven jump diffusion model. Our aim will be to estimate the drift on a compact set based on a high-frequency data sample.
Based on the available observations of Xt, we will construct an adaptive penalized least-squares estimate in order to compute an adaptive estimator of the corresponding drift function b. Under appropriate assumptions, we will bound the L2-risk of our proposed estimator. Moreover, we study the behavior of the proposed estimator in various Monte Carlo simulation setups.
Mathematics Subject Classification: 62M09 / 62G08
Key words: Adaptive estimation / integrated jump diffusion / drift estimation / model selection / mean square estimator
© EDP Sciences, SMAI 2019
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