A Multivariate Realized GARCH Model

We propose a novel class of multivariate GARCH models that utilize realized measures of volatilities and correlations. The central component is an unconstrained vector parametrization of the correlation matrix that facilitates modeling of the correlation structure. The parametrization is based on the matrix logarithmic transformation that retains the positive definiteness as an innate property. A factor approach offers a way to impose a parsimonious structure in high dimensional system and we show that a factor framework arises naturally in some existing models. We apply the model to returns of nine assets and employ the factor structure that emerges from a block correlation specification. An auxiliary empirical finding is that the empirical distribution of parametrized realized correlations is approximately Gaussian. This observation is analogous to the well-known result for logarithmically transformed realized variances.