Title: Nonparametric Gaussian inference for stable processes
Authors: Fabian Mies - RWTH Aachen University (Germany) [presenting]
Ansgar Steland - University Aachen (Germany)
Abstract: Jump processes driven by $\alpha$-stable Levy processes impose inferential difficulties as their increments are heavy-tailed and the intensity of jumps is infinite. We consider the estimation of the functional drift and diffusion coefficients from high-frequency observations of a stochastic differential equation. By transforming the increments suitably prior to a regression, the variance of the emerging quantities may be bounded while allowing for identification of drift and diffusion in the limit. The findings are applied to obtain a comprehensive treatment of the asymptotics of a nonparametric kernel estimator, covering asymptotic normality and consistency of subsampling approximations, and of a parametric volatility estimator for the Ornstein-Uhlenbeck process. The proposed approach also suggests a semiparametric estimator for the index of stability $\alpha$.