The conditional standard deviation, or volatility, of asset returns evolves over time; financial volatilities move together over time across assets and markets. For even a handful of assets, the curse of dimensionality quickly makes extimation of most multivariate models impractical. We apply and extend methods from independent component analysis and from the generalized method of moments to effectively reduce the estimation probelm to a set of disjoint univariate models. Our multivariate conditional heteroscedastic model allows exact or stochastic parameterizations as well as asymmetry in the respective volatility series. Correlations evolve over time without explicit modeling, and the estimated volatility matrix is positivve-definite at every time index. This tallk is based on joint work with Ruey S. Tsay.