local polynomial estimation of time-dependent diffusion parameter for discretely observed SDE models

Abstract

Extending the results of Yu et al.(2009), we study the local polynomial estimation of the time-dependent diffusion parameter for time-inhomogeneous diffusion models. Considering the diffusion parameter being positive, we obtain the local polynomial estimation of the diffusion parameter by taking the diffusion parameter to be local log-polynomial fitting. Asymptotic bias, asymptotic variance and asymptotic normal distribution of volatility function are discussed.