Nonparametric estimation of jump diffusion models

Abstract

This paper develops the asymptotics for nonparametric kernel estimators of local time, drift and volatilities, and Lévy measure in jump diffusion models. Our asymptotics are developed in a very general set-up, allowing the sample span to increase as the sampling interval decreases, and without assuming stationarity. For drift and volatilities, we analyze both local constant and local linear estimators. We consider not only estimators for instantaneous conditional second moment, but also threshold estimators to disentangle diffusive and jump volatilities. The optimal bandwidths are provided for all these estimators.