Local Linear Estimations of Time-Varying Parameters for Time-Inhomogeneous Diffusion Models

This paper studies the local linear estimations of the time-varying parameters for time-inhomogeneous diffusion models. Based on discretely observed sample of time-inhomogeneous diffusion models, the local linear estimations of the drift parameters are proposed and their standard errors are discussed. Considering the volatility parameter being positive, we obtain the kernel weighted estimation of the diffusion parameter by using locally log-linear fitting, and discuss asymptotic bias, asymptotic variance and asymptotic normal distribution of volatility function. It is shown that the local estimations proposed perform well through simulation studies.