Non-parametric estimation of the coefficients of ergodic diffu- sion processes based on high-frequency data

UFR de Mathe´matiques et Informatique, Universite´ Paris Descartes – Paris 5 45 rue des Saints-Pe`res, 75270 Paris cedex 06, France

5.1 Introduction

The content of this chapter is directly inspired by Comte, Genon-Catalot, and Rozenholc (2006; 2007). We consider non-parametric estimation of the drift and diffusion coefficients of a one-dimensional diffusion process. The main assumption on the diffusion model is that it is ergodic and geometrically βmixing. The sample path is assumed to be discretely observed with a small regular sampling interval ∆. The estimation method that we develop is based on a penalized mean square approach. This point of view is fully investigated for regression models in Comte and Rozenholc (2002, 2004). We adapt it to discretized diffusion models.