Nonparametric Estimation for the Diffusion Coefficent of Continuous-time Models with Noisy High-Frequency Data

Recent advances in financial econometrics have led to the development of new estimators of the diffusion coefficient by using frequently-sampled price data. These estimators rely on a variety of different assumptions and take many different functional forms in time and state domains. Motivated by the empirical and theoretical success of combination estimation based on time-domain and state-domain, this paper presents new results by combining individual estimators to form the new estimators of the diffusion coefficient. The proposed estimators eliminate the effects of the market microstructure noise and Monte Carlo analysis demonstrates their finite sample performances. Under certain conditions, some asymptotic properties are derived here. We find that these estimators can generally be outperformed, in terms of accuracy, by any individual estimator and the existing integrated estimators.