Explaining Epps Effect When Bivariate Price Staleness Is Present

The intraday high-frequency datasets contain several zero returns, which state that no change occurs in two or more consecutive transactions, particularly in the transaction data of in- active securities. In addition, existing approaches to cleaning financial data, such as the previous-tick method, induce zero returns. It has been shown by Phillips and Yu (2007) and Buccheri et al. (2020) that the presence of zero returns affects the limiting behavior of realized power variations and realized covariation of semi-martingale. In this study, we establish a unified result for the limiting theory of the realized power variations of multivari- ate semi-martingales, which includes the results of Phillips and Yu (2007) as a special case. Moreover, we provide a new asymptotic theory for realized covariation by considering the bivariate price staleness processes between assets. A Monte Carlo study verifies the proposed theory, and an analysis of real high-frequency data is proposed for illustration purposes.