Nonparametric Estimation of Diffusion Processes with Discrete Observations

This paper makes three contributions to the literature on the nonparametric estimation of diffusion processes. First, we show that the nonparametric estimator of the drift function proposed by Stanton (J. of Finance, 1997) is not consistent. Second, we show that a proposed alternative nonparametric estimator of the drift function converges to the true drift in probability, in addition to providing the rate of convergence. Finally we show that, under certain conditions, a nonparametric estimator of the drift and diffusion functions can be obtained while relaxing the assumption of bounded restrictions on both drift and diffusion functions.