Asymmetric models for realized covariances

We introduce asymmetric effects in the BEKK-type conditional autoregressive Wishart model for realized covariance matrices, either by interacting the realized covariances with the signs of the daily returns or by using the decomposition of the realized covariance matrix into positive, negative, and mixed semi-covariances, thus relying on the signs of the intra-daily returns. In an empirical study, we find that the asymmetric models using the signs of the daily returns have a better in-sample fit and out-of-sample predictive ability than the models using the signed intra-daily returns, and that the asymmetric models outperform the symmetric one.