Nonparametric Combining Estimation of the Diffusion Coefficient of Diffusion Models

In order to improve the accuracy of the diffusion coefficient estimation, we propose a new combining estimator to estimate the diffusion coefficient by dynamically integrating information from the time-domain and the state-domain. We find that the proposed estimator can effectively estimate the diffusion coefficient of diffusion models, as we show in this paper on simulated time series. Under certain conditions, the asymptotic normality is separately established for the proposed nonparametric estimators and the proposed theorem proves that the time-domain and state-domain estimators are asymptotically independent. Extensive simulations demonstrate the proposed estimator outperforms the other two estimators, and also outperforms the ones in the literature.