2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130786We 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.37 pages, 8 figuresStatistics Theory62H12text