When Asynchronicity Meets Price Staleness: Robust Estimation of High-Frequency Covariance

The Epps effect refers to the empirical decline in measured asset dependence as the sampling frequency increases. Existing studies have shown that market microstructure frictions, including asynchronous trading and price staleness, can contribute to this downward bias in high-frequency covariance estimation. In this study, we propose a novel estimator of high-frequency covariance that is robust to the concurrent presence of asynchronicity and price staleness. We establish the asymptotic properties of the proposed estimator and present a feasible central limit theorem that accommodates time-varying staleness probabilities. The proposed robust covariance estimator also yields consistent estimators of beta and correlation in the presence of these anomalies. In addition, we adopt a pre-averaging method to address microstructure noise. Through theoretical analysis and Monte Carlo simulations, we demonstrate that our estimator significantly outperforms existing alternatives. Empirically, using tick-by-tick data, we evaluate ETF tracking performance across various covariance estimators. The results highlight the superiority and robustness of the proposed estimator. JEL Classification: C58, C32