We introduce a multivariate GARCH model that incorporates realized measures of volatility and covolatility. The realized measures extract information about the current level of volatility and covolatility from high-frequency data, which is particularly useful for the modeling of return...

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...