Efficient Covariance Estimation for Asynchronous Noisy High-Frequency Data


Markus Bibinger, Department of Mathematics, Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, Germany.
E-mail: bibinger@math.hu-berlin.de


Abstract.  We focus on estimating the integrated covariance of log-price processes in the presence of market microstructure noise. We construct a consistent asymptotically unbiased estimator for the quadratic covariation of two Itô processes in the case where high-frequency asynchronous discrete returns under market microstructure noise are observed. This estimator is based on synchronization and multi-scale methods and attains the optimal rate of convergence. A lower bound for the rate of convergence is derived from the local asymptotic normality property of the simpler parametric model with equidistant and synchronous observations. A Monte Carlo study analyses the finite sample size characteristics of our estimator.