We propose a least squares regression framework for the estimation of the realized covariation matrix using high frequency data. The new estimator is robust to market microstructure noise (MMS) and non-synchronous trading. Comprehensive simulation and empirical analysis show that our estimator performs as well as a set of popular estimators in the literature. More importantly, our framework allows for the unique identification of MMS noise moments. We find that these noise moments are related to measures of liquidity and contain predictive information that helps to significantly improve out-of-sample asset allocation.