Nonparametric Estimation of the Drift Coefficient of a Stochastic Diffusion Process in the Presence of Measurement Error

We propose a Nadaraya-Watson type kernel estimator of the drift coefficient of a diffusion process, where the process is observed discretely in time and with independent additive measurement errors. Our estimation procedure first averages the data neighboring in time, therefore reducing the noise caused by the measurement errors and revealing the latent diffusion process. We show that our estimator is consistent and asymptotically normal when the diffusion process is positive recurrent and strictly stationary and the independent additive measurement errors have zero mean and bounded variance. We study the properties of our estimator via simulation.