Nonsynchronous covariation process and limit theorems

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Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence (2014, methodology): “They bear some resemblance to the pre-averaged returns as employed in Jacod et al. (2009). While pre-averaging estimators, however, utilize rolling (local) windows around each observation, our approach relies on fixed blocks and optimal combinations in the spectral frequency domain.”
Estimating the Quadratic Covariation Matrix from Noisy Observations: Local Method of Moments and Efficiency (2013, background): “This is in sharp contrast to the noiseless setting where the variance of the Hayashi–Yoshida estimator [14] suffers from errors due to asynchronicity, which carries over to the pre-averaged version by Christensen et al. [9] designed for the noisy case.”
Adaptive estimation of continuous-time regression models using high-frequency data (2017, background): “…regression estimation in the case when the data is contaminated by noise and the elements of X are asynchronously observed; see, for example, Hayashi and Yoshida (2011) and Bibinger et al. (2014) for ways to handle such complications in the data in the context of volatility…”
An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory (2011, unknown): “A similar stable limit theorem for the original Hayashi-Yoshida estimator is provided in [17].”