| Issue |
ESAIM: PS
Volume 22, 2018
|
|
|---|---|---|
| Page(s) | 236 - 260 | |
| DOI | https://doi.org/10.1051/ps/2018005 | |
| Published online | 25 January 2019 | |
Research article
Adaptive nonparametric drift estimation of an integrated jump diffusion process
1
TU Dortmund, Faculty of Mathematics,
44227
Dortmund, Germany .
2
Université Lille 1, Laboratoire Paul Painlevé,
59655
Villeneuve d’Ascq, France .
* Corresponding author: benedikt.funke@math.tu-dortmund.de
Received:
25
May
2017
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.
Instead of observing the jump diffusion process V itself, we observe a discrete and high-frequent sample of the integrated process
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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