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This paper suggests a new approach to evaluate realized covariance (RCOV) estimators via their predictive power on return density. By jointly modeling returns and RCOV measures under a Bayesian framework, the predictive density of returns and ex-post covariance measures are bridged. The forecast performance of a covariance estimator can be assessed according to its improvement in return density forecasting. Empirical applications to equity data show that several RCOV estimators consistently perform better than others and emphasize the importance of RCOV selection in covariance modeling and forecasting.

Does the Choice of Realized Covariance Measures Empirically Matter? A Bayesian Density Prediction Approach