Unbiased covariance estimation with interpolated data

We study covariance estimation when compelled to use evenly spaced data which have already been manipulated by previous-tick interpolation. We propose an un- biased covariance estimator, which is designed to correct for the two biases arising because of the interpolation: non-synchronous trading and zero-return bias. We show how these sources make usual realized covariance estimators biased, and that the traditional lead-lag modification does not correct these biases completely. The proposed estimator is also proved to be consistent with the Hayashi and Yoshida (2005)’s unbiased estimator under extremely high frequency situation. We illustrate the potential advantages of the method with both simulated and actual data