In the present article, we investigate nonparametric estimation of the unknown drift function 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 itself, we observe a discrete and high-frequent sample of the integrated process
Based on the available observations of , we will construct an adaptive penalized least-squares estimate in order to compute an adaptive estimator of the corresponding drift function . Under appropriate assumptions, we will bound the -risk of our proposed estimator. Moreover, we study the behavior of the proposed estimator in various Monte Carlo simulation setups.
Keywords: Adaptive estimation, integrated jump diffusion, drift estimation, model selection, mean square estimator
Funke, Benedikt 1 ; Schmisser, Émeline 1
@article{PS_2018__22__236_0,
author = {Funke, Benedikt and Schmisser, \'Emeline},
title = {Adaptive nonparametric drift estimation of an integrated jump diffusion process},
journal = {ESAIM: Probability and Statistics},
pages = {236--260},
year = {2018},
publisher = {EDP Sciences},
volume = {22},
doi = {10.1051/ps/2018005},
mrnumber = {3903643},
zbl = {1409.62161},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2018005/}
}
TY - JOUR AU - Funke, Benedikt AU - Schmisser, Émeline TI - Adaptive nonparametric drift estimation of an integrated jump diffusion process JO - ESAIM: Probability and Statistics PY - 2018 SP - 236 EP - 260 VL - 22 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2018005/ DO - 10.1051/ps/2018005 LA - en ID - PS_2018__22__236_0 ER -
%0 Journal Article %A Funke, Benedikt %A Schmisser, Émeline %T Adaptive nonparametric drift estimation of an integrated jump diffusion process %J ESAIM: Probability and Statistics %D 2018 %P 236-260 %V 22 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps/2018005/ %R 10.1051/ps/2018005 %G en %F PS_2018__22__236_0
Funke, Benedikt; Schmisser, Émeline. Adaptive nonparametric drift estimation of an integrated jump diffusion process. ESAIM: Probability and Statistics, Tome 22 (2018), pp. 236-260. doi: 10.1051/ps/2018005
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