Adaptive nonparametric drift estimation of an integrated jump diffusion process

Funke, Benedikt; Schmisser, Émeline

ESAIM: Probability and Statistics, Tome 22 (2018), pp. 236-260.

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

$$X_t:={\int }_0^t{V}_s\mathrm{d}s$$

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.

Classification : 62M09, 62G08
Mots clés : Adaptive estimation, integrated jump diffusion, drift estimation, model selection, mean square estimator

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