In this paper, we develop econometric tools to analyze the integrated volatility (IV) of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent estimators of the variance and autocovariances of noise using a variant of realized volatility. Next, we employ these estimators to adapt the pre-averaging method and derive consistent estimators of the IV, which converge stably to a mixed Gaussian distribution at the optimal rate n 1/4 . To improve the finite sample performance, we propose a multi-step approach that corrects the finite sample bias, which turns out to be crucial in applications. Our extensive simulation studies demonstrate the excellent performance of our multi-step estimators. In an empirical study, we analyze the dependence structures of microstructure noise and provide intuitive economic interpretations; we also illustrate the importance of accounting for both the serial dependence in noise and the finite sample bias when estimating IV.

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We introduce a new method to estimate the integrated volatility (IV) based on noisy highfrequency data. Our method employs the ReMeDI approach introduced by Li and Linton (2021a) to estimate the moments of the microstructure noise and thereby eliminate their influence, and the pre-averaging method to target the volatility parameter. The method is robust: it can be applied when the efficient price exhibits stochastic volatility and jumps, the observation times are random and endogenous, and the noise process is nonstationary, autocorrelated and dependent on the efficient price. We derive the limit distribution for the proposed estimators under infill asymptotics in a general setting. Our simulation and empirical studies demonstrate the robustness, accuracy and computational efficiency of our estimators compared to several alternatives recently proposed in the literature.