We show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an asymptotic theory for this new estimator, which can be...

We show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an asymptotic theory for this new estimator, which can be...

In this paper we present the central limit theorem for general functions of the increments of Brownian semimartingales. This provides a natural extension of the results derived in Barndorff-Nielsen, Graversen, Jacod, Podolskij and Shephard (2006), who showed the central limit theorem for even...

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...

Central limit theorem, quadratic variation, bipower variation

An urn contains balls of d = 2 colors. At each time n = 1, a ball is drawn and then replaced together with a random number of balls of the same color. Let An =diag (An,1, . . . ,An,d) be the n-th reinforce matrix. Assuming EAn,j = EAn,1 for all n and j, a few CLT's are available for such urns....