The Annals of Statistics

Asymptotic equivalence for inference on the volatility from noisy observations

Markus Reiß

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Abstract

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

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

Dates
First available in Project Euclid: 9 March 2011

Permanent link to this document
http://projecteuclid.org/euclid.aos/1299680954

Digital Object Identifier
doi:10.1214/10-AOS855

Zentralblatt MATH identifier
1215.62113

Mathematical Reviews number (MathSciNet)
MR2816338

Subjects
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]

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

Citation

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. http://projecteuclid.org/euclid.aos/1299680954.


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