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 estimatio n procedure for an Ito diffusion process based on discrete sampling ob servations. The nonparametric kernel estimator for the diffusion funct ion developed in this paper deals with general Ito diffusion processes and avoids any functional form specification for either the drift fun ction or the diffusion function. It is shown that under certain regula rity conditions the nonparametric diffusion function estimator is poin twise consistent and asymptotically follows a normal mixture distribut ion. Under stronger conditions, a consistent nonparametric estimator o f the drift function is also derived based on the diffusion function e stimator and the marginal density of the process, An application of th e nonparametric technique to a short-term interest rate model involvin g Canadian daily 3-month treasury bill rates is also undertaken. The e stimation results provide evidence for rejecting the common parametric or semiparametric specifications for both the drift and diffusion fun ctions.