We consider the estimation of integrated covariance (ICV) matrices of high dimensional diffusion processes based on high frequency observations. We start by studying the most commonly used estimator, the realized covariance (RCV) matrix. We show that in the high dimensional case when the...

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...

This paper introduces a new approach to constructing optimal mean-variance portfolios. The approach relies on a novel unconstrained regression representation of the mean-variance optimization problem combined with high-dimensional sparse-regression methods. Our estimated portfolio, under a mild...

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,...

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 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 develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem for linear spectral statistics of the sample covariance matrix based on self-normalized observations. For testing sphericity, our tests neither assume...

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....

For many multi-factor asset pricing models proposed in the recent literature, their implied tang-ency portfolios have substantially higher sample Sharpe ratios than that of the value-weighted market portfolio. In contrast, such high sample Sharpe ratio is rarely delivered by professional fund...

We study the estimation of the high-dimensional covariance matrix and its eigenvalues under dynamic volatility models. Data under such models have nonlinear dependency both cross-sectionally and temporally. We first investigate the empirical spectral distribution (ESD) of the sample covariance...