This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise, which are observed at high frequency. Our method generalizes the pre-averaging approach (see [13],[11]) and provides consistent estimates for various characteristics of general...

We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices. We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to measurement noise of certain types and can also handle non-synchronous trading. It is the first estimator...

We propose a new measure of risk, based entirely on downwards moves measured using high frequency data. Realised semivariances are shown to have important predictive qualities for future market volatility. The theory of these new measures is spelt out, drawing on some new results from...

We propose a new measure of risk, based entirely on downward moves measured using high frequency data.  Realised semivariances are shown to have important predictive qualities for future market volatility.  The theory of these new measures is spelt out, drawing on some new results from...

We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices.  We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to measurement noise of certain types and can also handle non-synchronous trading.  It is the first...