  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 we may fit each CUC 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 test is proposed for testing the existence of
CUCs. The proposed methodology is illustrated with both simulated and real data
sets.
