Open Access
April 2011 Asymptotic equivalence for inference on the volatility from noisy observations
Markus Reiß
Ann. Statist. 39(2): 772-802 (April 2011). DOI: 10.1214/10-AOS855


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.


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Markus Reiß. "Asymptotic equivalence for inference on the volatility from noisy observations." Ann. Statist. 39 (2) 772 - 802, April 2011.


Published: April 2011
First available in Project Euclid: 9 March 2011

zbMATH: 1215.62113
MathSciNet: MR2816338
Digital Object Identifier: 10.1214/10-AOS855

Primary: 62B15 , 62G20 , 62M10 , 91B84

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

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 2 • April 2011
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