Nonparametric estimation of a scalar diffusion model from discrete time data: a survey

In view of rapid developments on nonparametric estimation of the drift and volatility functions in scalar diffusion models in financial econometrics, from discrete-time observations, we provide, in this paper, a survey of its state-of-the-art with new insights into current practices, as well as elaborating on our own recent contributions. In particular, in presenting the main principles of estimation for both stationary and nonstationary cases, we show the possibility to estimate nonparametrically the drift and volatility functions without distinguishing these two frameworks.