A Nonparametric Approach to the Estimation of Diffusion Processes - With an Application to a Short-Term Interest Rate Model

In this paper, we propose a nonparametric identification and estimation procedure for an It6 diffusion process based on discrete sampling observations. The nonparametric kernel estimator for the diffusion function developed in this paper deals with general It6 diffusion processes and avoids any functional form specification for either the drift function or the diffusion function. It is shown that under certain regularity conditions the nonparametric diffusion function estimator is pointwise consistent and asymptotically follows a normal mixture distribution. Under stronger conditions, a consistent nonparametric estimator of the drift function is also derived based on the diffusion function estimator and the marginal density of the process. An application of the nonparametric technique to a short-term interest rate model involving Canadian daily 3-month treasury bill rates is also undertaken. The estimation results provide evidence for rejecting the common parametric or semiparametric specifications for both the drift and diffusion functions