Estimation for high-frequency data under parametric market microstructure noise
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In this paper, we propose a general class of noise-robust estimators based on the existing estimators in the non-noisy high-frequency data literature. The market microstructure noise is a known parametric function of the limit order book. The noise-robust estimators are constructed as a plug-in version of their counterparts, where we replace the efficient price, which is non-observable in our framework, by an estimator based on the raw price and the limit order book data. We show that the technology can be directly applied to estimate volatility, high-frequency covariance, functionals of volatility and volatility of volatility in a general nonparametric framework where, depending on the problem at hand, price possibly includes infinite jump activity and sampling times encompass asynchronicity and endogeneity.
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