Before revision:  However, secondly, since multivariate asset returns are not traded synchronously , we have to use  largest time intervals so that all asset returns are observed  to compute the realized covariance matrices , where we fail to make full use of  available intraday informations when there are less frequently traded assets.
After revision:  Second, since multivariate asset returns are not traded synchronously , we have to use largest time intervals so that all asset returns are observed to compute the realized covariance matrices , where we fail to make full use of available intraday informations when there are less frequently traded assets.