Models with Time-Varying Parameters for Realized Covariance

Several recent contributions in econometrics and statistics deal with the dynamic modelling of conditional covariance matrices. To guarantee the positive definiteness of the estimated covariance matrices and to obtain parsimonious models, most of the models proposed use scalar parameterizations that involve a small number of parameters, but have the drawback to impose constraints that may strongly restrict the flexibility of the dynamics of the conditional covariance or correlation process. Using the properties of the Hadamard exponential functions, we develop parsimonious but flexible models, which provide positive definite covariance matrices with different and time varying coefficients for each element of the covariance matrix. Their properties are verified with an empirical exercise, using realized covariance daily data for 29 assets.