期刊
ANNALS OF STATISTICS
卷 39, 期 2, 页码 772-802出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/10-AOS855
关键词
High-frequency data; diffusions with measurement error; microstructure noise; integrated volatility; spot volatility estimation; Le Cam deficiency; equivalence of experiments; Gaussian shift
We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function a and a nonstandard noise level. As an application, new rate-optimal estimators of the volatility function and simple efficient estimators of the integrated volatility are constructed.
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