Test of Unbiasedness of the Integrated Covariance Estimation in the Presence of Noise

The cumulative covariance estimator in Hayashi and Yoshida (2005b) which suits for non-synchronous observations possibly has a bias in the presence of the observational noise. We propose the test statistic to detect whether the observational noise causes a measurable bias in the estimator of Hayashi and Yoshida (2005b). The test statistic proposed in this paper is asymptotically distributed as standard normal under null hypothesis. The finite sample performance of the test statistic is investigated through Monte Carlo simulation.