Modeling Multivariate Volatilities via Conditionally Uncorrelated Components

We propose to model multivariate volatility processes based on the newly defined conditionally uncorrelated components (CUCs). This model represents a parsimonious representation for matrix-valued processes. It is flexible in the sense that each CUC may be fitted separately with any appropriate univariate volatility model. Computationally it splits one high-dimensional optimization problem into several lower-dimensional subproblems. Consistency for the estimated CUCs has been established. A bootstrap method is proposed for testing the existence of CUCs. The proposed methodology is illustrated with both simulated and real data sets.