Nonparametric drift estimation in a Lévy driven diffusion model

Abstract

In this article, a pointwise nonparametric kernel based estimator for the drift function in a Levy driven jump diffusion model is proposed. Under ergodicity and stationarity of the underlying process X, we derive asymptotic properties as consistency and asymptotic normality of the estimator. In addition, we propose a consistent estimator of the asymptotic variance. Moreover, we show that this approach is robust under microstructure noise by using the preaveraging approach proposed in Podolskij and Vetter (2006).