Pre-averaging is a popular strategy for mitigating microstructure in high frequency financial data. As the term suggests, transaction or quote data are averaged over short time periods ranging from 30 seconds to five minutes, and the resulting averages approximate the efficient price process...

In this paper, we derive a new algebraic property of two scales estimation in high frequency data, under which the effect of sampling times is cancelled to high order. This is a particular robustness property of the two scales construction. In general, irregular, asynchronous, or endogenous...

We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel Q. Special cases include additive error, rounding, and combinations thereof. Our main result is that, subject to smoothness conditions, the two scales realized volatility...