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

Extending the results of Yu, Yu, Wang and Lin [10], 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. The asymptotic bias, asymptotic variance and asymptotic normal distribution of the volatility function are discussed. A real data analysis is conducted to show the performance of the estimations proposed.