ASYMPTOTIC EQUIVALENCE FOR INFERENCE ON THE VOLATILITY FROM NOISY OBSERVATIONS

• 成果类型: Article
• 署名作者: Reiss, Markus
• 署名单位: Humboldt University of Berlin
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS855
• 发表日期: 2011
• 页码: 772-802
• 关键词: Nonparametric regression; microstructure noise

摘要

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.