Estimation for high-frequency data under parametric market microstructure noise
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Estimation for high‑frequency data under parametric market microstructure noise Simon Clinet1 · Yoann Potiron2 Received: 11 September 2019 / Revised: 4 August 2020 © The Institute of Statistical Mathematics, Tokyo 2020
Abstract We develop a general class of noise-robust estimators based on the existing estimators in the non-noisy high-frequency data literature. The microstructure noise is a parametric function of the limit order book. The noise-robust estimators are constructed as plug-in versions of their counterparts, where we replace the efficient price, which is non-observable, by an estimator based on the raw price and limit order book data. We show that the technology can be applied to five leading examples where, depending on the problem, price possibly includes infinite jump activity and sampling times encompass asynchronicity and endogeneity. Keywords Functionals of volatility · High-frequency covariance · High-frequency data · Limit order book · Parametric market microstructure noise
1 Introduction It is now widely acknowledged that the availability of high-frequency data has led to a more accurate description of financial markets. Over the past decades, empirical studies have unveiled several aspects of the frictionless efficient price. Accordingly, the assumptions on the latter have been gradually weakened to the extent that it is common nowadays to represent it as a general Itô semi-martingale including Electronic supplementary material The online version of this article (https://doi.org/10.1007/s1046 3-020-00762-3) contains supplementary material, which is available to authorized users. * Simon Clinet [email protected] http://user.keio.ac.jp/~clinet/ Yoann Potiron [email protected] http://www.fbc.keio.ac.jp/~potiron 1
Faculty of Economics, Keio University, 2‑15‑45 Mita, Minato‑ku, Tokyo 108‑8345, Japan
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Faculty of Business and Commerce, Keio University, 2‑15‑45 Mita, Minato‑ku, Tokyo 108‑8345, Japan
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jumps with infinite activity. Moreover, the sampling times are also often considered as asynchronous, random, and even sometimes endogenous, i.e. possibly correlated with the efficient price. The accessibility of high-frequency data has also shed light on the frictions, or so-called market microstructure noise (MMN), which get prominent as the sampling frequency increases. As a matter of fact, realized volatility (i.e. summing the square returns), which is efficient in the absence of frictions, becomes badly biased when the frequency increases. This was visible on the signature plot in Andersen et al. (2001a). A typical challenge that faces a theoretical statistician today is to incorporate jumps, asynchronicity, endogeneity and frictions into the model. A frequently used set-up is
Zti = Xti + 𝜖ti , ⏟⏟⏟ ⏟⏟⏟ ⏟⏟⏟ observed price
efficient price
MMN
(1)
where 𝜖ti is i.i.d. and latent. In two nice and independent papers, Li et al. (2016) and Chaker (2017), and subsequently Clinet and Potiron (2019a, b), consider the following parametric form
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