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

Fabienne Comte (1) , Valentine Genon-Catalot (1) , Yves Rozenholc (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

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 β- mixing. 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.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Fabienne Comte, Valentine Genon-Catalot, Yves Rozenholc. Non-parametric estimation of the coefficients of ergodic diffusion processes based on high-frequency data. M. Kessler, A. Lindner, M. Sorensen. Statistical Methods for Stochastic Differential Equations, Chapman & Hall/CRC Monographs on Statistics & Applied Probability, pp.341-381, 2012, SemStat series. ⟨hal-00748939⟩