We consider a setting where market microstructure noise is a parametric function of trading information, possibly with a remaining noise component. Assuming that the remaining noise is $O_p(1/\sqrt{n})$, allowing irregular times and jumps, we show that we can estimate the parameters at rate $n$,...

We study the estimation of (joint) moments of microstructure noise based on high frequency data. The estimation is conducted under a nonparametric setting, which allows the underlying price process to have jumps, the observation times to be irregularly spaced, \emph{and} the noise to be...

We develop a volatility estimator that can be directly applied to tick-by-tick data. More specifically, we consider a model that allows for (i) irregular observation times that can be endogenous, (ii) dependent noise that can have diurnal features and be dependent on the latent price process,...

This paper presents a generalized pre-averaging approach for estimating the integrated volatility. This approach also provides consistent estimators of other powers of volatility in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the...