Geodesic
Adaptive nonparametric drift estimation of an integrated jump diffusion process
ESAIM: Probability and Statistics, Tome 22 (2018), pp. 236-260

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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

X t : = ∫ 0 t V s d s

Based on the available observations of X t , 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 L 2 -risk of our proposed estimator. Moreover, we study the behavior of the proposed estimator in various Monte Carlo simulation setups.

DOI : 10.1051/ps/2018005
Classification : 62M09, 62G08
Keywords: Adaptive estimation, integrated jump diffusion, drift estimation, model selection, mean square estimator

Funke, Benedikt 1 ; Schmisser, Émeline 1

1 
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     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},
     publisher = {EDP-Sciences},
     volume = {22},
     year = {2018},
     doi = {10.1051/ps/2018005},
     mrnumber = {3903643},
     zbl = {1409.62161},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2018005/}
}
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%A Schmisser, Émeline
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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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