Robust Estimation of Integrated and Spot Volatility

We introduce a new method to estimate the integrated volatility (IV) and the spot volatility (SV) based on noisy high-frequency data. Our method employs the ReMeDI approach introduced by Li and Linton (2022a) to estimate the moments of 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 the noise process is nonstationary, autocorrelated, asymptotically vanishing and dependent on the efficient price. We derive the limit distributions for the proposed estimators under the infill asymptotics in a general setting. Our extensive simulation studies demonstrate the robustness, accuracy and computational efficiency of our estimators compared to several alternative estimators recently proposed in the literature. Empirically, we show that neglecting the complexities of noise and the random observation times yields substantial biases in volatility estimation and may lead to a different intraday volatility pattern.