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

This paper studies the local linearestimations of the time-varying parameters for time-inhomogeneousdiffusion models. Based on discretely observed sample oftime-inhomogeneous diffusion models, the local linear estimations ofthe drift parameters are proposed and their standard errors arediscussed. Considering the volatility parameter being positive, weobtain the kernel weighted estimation of the diffusion parameter byusing locally log-linear fitting, and discuss asymptotic bias,asymptotic variance and asymptotic normal distribution of volatilityfunction. It is shown that the local estimations proposed performwell through simulation studies.