Adaptive nonparametric drift estimation of an integrated jump diffusion process
Résumé
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 unknown drift function 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 Xt := t 0 Vsds. 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 L 2-risk of our proposed estimator. Moreover , we study the behavior of the proposed estimator in various Monte Carlo simulation setups.
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