Research article

Adaptive nonparametric drift estimation of an integrated jump diffusion process

¹ TU Dortmund, Faculty of Mathematics, 44227 Dortmund, Germany .
² Université Lille 1, Laboratoire Paul Painlevé, 59655 Villeneuve d’Ascq, France .

^* Corresponding author: benedikt.funke@math.tu-dortmund.de

Received: 25 May 2017
Accepted: 16 January 2018

Abstract

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 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 L²-risk of our proposed estimator. Moreover, we study the behavior of the proposed estimator in various Monte Carlo simulation setups.