Estimation of diffusion parameters for discretely observed diffusion processes

Abstract

We study the estimation of diffusion parameters for one-dimensional, ergodic diffusion processes that are discretely observed. We discuss a method based on a functional relationship between the drift function, the diffusion function and the invariant density and use empirical process theory to show that the estimator is $\sqrt{n}$-consistent and in certain cases weakly convergent. The Chan-Karolyi-Longstaff-Sanders (CKLS) model is used as an example and a numerical example is presented.