Semiparametric Estimation of Locally Stationary Diffusion Models

This paper proposes a class of locally stationary diffusion processes. The model has a time varying but locally linear drift and a volatility coefficient that is allowed to vary over time and space. We propose estimators of all the unknown quantities based on long span data. Our estimation method makes use of the local stationarity. We establish asymptotic theory for the proposed estimators as the time span increases. We apply this method to the real financial data to illustrate the validity of our model. Finally, we present a simulation study to provide the finitesample performance of the proposed estimators