The Annals of Statistics
- Ann. Statist.
- Volume 39, Number 2 (2011), 772-802.
Asymptotic equivalence for inference on the volatility from noisy observations
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 σ 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.
Ann. Statist., Volume 39, Number 2 (2011), 772-802.
First available in Project Euclid: 9 March 2011
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G20: Asymptotic properties 62B15: Theory of statistical experiments 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 91B84: Economic time series analysis [See also 62M10]
Reiß, Markus. Asymptotic equivalence for inference on the volatility from noisy observations. Ann. Statist. 39 (2011), no. 2, 772--802. doi:10.1214/10-AOS855. https://projecteuclid.org/euclid.aos/1299680954