Efficient and positive semidefinite pre-averaging realized covariance estimator

We propose a realized-covariance estimator based on efficient multiple pre-averaging (EMP) for asynchronous and noisy high-frequency data. The EMP estimator is consistent, guaranteed to be positive-semidefinite, and achieves the optimal convergence rate at n⁻1/⁴. It is constructed based on 1) an innovative synchronizing technique that uses all available price information, and 2) an eigenvalue correction method that ensures positive-semidefiniteness without sacrificing the optimal convergence rate. A simulation study demonstrates the good performance of the EMP estimator for finite samples in terms of accuracy, properties, and convergence rate. In a real-data analysis, the EMP covariance estimator delivers performance that is more stable than that of alternative estimators. The new estimator also outperforms alternative realized-covariance estimators in terms of portfolio selection.