Diffusion Copulas: Identification and Estimation

We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed processes are nonparametric transformations of underlying parametric diffusions (UPDs). This modelling strategy yields a general class of semiparametric Markov diffusion models with parametric dynamic copulas and nonparametric marginal distributions. We provide primitive conditions for the identification of the UPD parameters together with the unknown transformations from discrete samples. Semiparametric likelihood-based estimators of the UPD parameters are developed and we show that under regularity conditions both the parametric and nonparametric components converge with parametric rate towards Normal distributions. Kernel-based drift and diffusion estimators are also proposed and shown to be normally distributed in large samples. A simulation study investigates the Önite sample performance of our estimators in the context of modelling US short-term interest rates.