The Annals of Statistics

Asymptotic equivalence for inference on the volatility from noisy observations

Markus Reiß

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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.

Article information

Ann. Statist., Volume 39, Number 2 (2011), 772-802.

First available in Project Euclid: 9 March 2011

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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]

High-frequency data diffusions with measurement error microstructure noise integrated volatility spot volatility estimation Le Cam deficiency equivalence of experiments Gaussian shift


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.

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