Nonparametric Continuous Time Regressions with Functional Coefficients

This paper considers a continuous time regression with functional coefficients in conditional mean and variance functions, where the covariate of the regression is assumed to be a general recurrent diffusion. We propose a kernel-based nonparametric estimation for these functional coefficients using discretely sampled data from the underlying continuous time regression. We obtain the limiting behaviors of the proposed estimators through a two- dimensional asymptotic analysis while assuming a shrinking sampling interval and increasing time span and without the stationarity assumption. We demonstrate the feasibility our approach on a short-term interest rate model involving U.S. daily three-month treasury bill rates.