Modelling multivariate volatilities via conditionally uncorrelated components

We propose to model multivariate volatility processes based on the newly defined condi-tionally uncorrelated components (CUCs). This model represents a parsimonious represen-tation 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. Consis-tency 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. Key words: bootstrap test, causality in variance, dimension reduction, extended GARCH(1,1), financial returns, portfolio volatility, quasi-maximum likelihood estimator, time series. 1