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...

When estimating integrated volatilities based on high-frequency data, simplifying assumptions are usually imposed on the relationship between the observation times and the price process. In this paper, we establish a central limit theorem for the Realized Volatility in a general endogenous time...

Classical statistics suggest that for inference purposes one should always use as much data as is available. We study how the presence of market microstructure noise in high-frequency financial data can change that result. We show that the optimal sampling frequency at which to estimate the...