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: email@example.com
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.