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 propose a high dimensional minimum variance portfolio estimator under statistical factor models, and show that our estimated portfolio enjoys sharp risk consistency. Our approach relies on properly integrating l1 constraint on portfolio weights with an appropriate covariance matrix estimator....

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 studies the estimation of high-dimensional minimum variance portfolio (MVP) based on the high frequency returns which can exhibit heteroscedasticity and possibly be contaminated by microstructure noise. Under certain sparsity assumptions on the precision matrix, we propose estimators...