We develop the asymptotic theory for the realised power variation of the processes X = f • G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity condition on the path of...

In this paper, we show how simple pre-averaging can be applied to measure the ex-post covariance of high-frequency financial time series under market microstructure noise and non-synchronous trading. A modulated realised covariance based on pre-averaged data is proposed and studied in this...