ESTIMATION OF INTEGRATED COVARIANCES IN THE SIMULTANEOUS PRESENCE OF NONSYNCHRONICITY, MICROSTRUCTURE NOISE AND JUMPS

Abstract

We propose a new estimator for the integrated covariance of two Itô semimartingales observed at a high frequency. This new estimator, which we call the pre-averaged truncated Hayashi–Yoshida estimator, enables us to separate the sum of the co-jumps from the total quadratic covariation even in the case that the sampling schemes of two processes are nonsynchronous and the observation data are polluted by some noise. We also show the asymptotic mixed normality of this estimator under some mild conditions allowing infinite activity jump processes with finite variations, some dependency between the sampling times and the observed processes as well as a kind of endogenous observation error. We examine the finite sample performance of this estimator using a Monte Carlo study and we apply our estimators to empirical data, highlighting the importance of accounting for jumps even in an ultra-high frequency framework.