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Estimating Integrated Volatility Using High-Frequency Data with Zero Duration

     In estimating the integrated volatility using high-frequency data, it is well documented that the presence of the microstructure noise causes a big challenge. Recent literature has shown that the common feature of multiple observations brings an additional difficulty. In this paper, we show that the pre-averaging estimator is still consistent under the multiple observations, the related asymptotic distribution of the estimator is established. Besides, we also show that the PA estimator based on the multiple observations has some surprise properties, in some cases, it performs even better than the `ideal' estimator, by which we pretended we know the exact trading times of all transactions. Simulation studies justify the theoretical results, we also illustrate the estimator by a real data analysis.