Modeling Realized Covariance Matrices: A Class of Hadamard Exponential Models

Time series of realized covariance matrices can be modeled in the conditional autoregressive Wishart model family via dynamic correlations or via dynamic covariances. Extended parameterizations of these models are proposed, which imply a specific and time-varying impact parameter of the lagged realized covariance (or correlation) on the next conditional covariance (or correlation) of each asset pair. The proposed extensions guarantee the positive definiteness of the conditional covariance or correlation matrix with simple parametric restrictions, while keeping the number of parameters fixed or linear with respect to the number of assets. Two empirical studies reveal that the extended models have superior forecasting performances than their simpler versions and benchmark models.