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Statistica Sinica 31 (2021), 1441-1462


Liang-Ching Lin, Ying Chen, Guangming Pan and Vladimir Spokoiny

National Cheng Kung University, National University of Singapore,
Nanyang Technological University and Weierstrass Institute

Abstract: 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. 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.

Key words and phrases: Asynchronous and noisy high-frequency data, eigenvalue correction, synchronizing technique.

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