Asymmetric Models for Realized Covariances

We introduce asymmetric effects in the BEKK-type conditional autoregressive Wishart model for realized covariance matrices. The asymmetry terms are specified either by interacting the lagged realized covariances with the signs of the lagged daily returns or by using the decomposition of the lagged realized covariance matrix into positive, negative, and mixed semi-covariances, thus relying on the lagged intra-daily returns and their signs. We provide a detailed comparison of models with different complexity, for example with respect to restrictions on the parameter matrices. In an extensive empirical study, our results suggest that the asymmetric models outperform the symmetric one in terms of statistical and economic criteria. The asymmetric models using the signs of the daily returns tend to have a better in-sample fit and out-of-sample predictive ability than the models using the signed intra-daily returns.