On covariance estimation for high-frequency financial data

We consider the problem of estimating the covariance/correlation of two diffusion prices that are observed at discrete times in a nonsynchronous manner. The modem, popular approach in the literature, "realized" estimator, which is based on the sum of cross-products of intra-day log-price changes measured on regularly-spaced intervals over a day, is problematic because choice of regular interval size and data interpolation scheme may lead to unreliable estimation. We present a new estimation procedure recently proposed by [1], which is free of such "synchronization" of data, hence, free from biases or other problems caused by it. In particular, our estimators are shown to have consistency as the observation frequency (or the market liquidity) tends to infinity, which is not possessed by the realized estimators.