TVICA: Time varying independent component analysis and its applications to financial data. A new method of ICA, TVICA, is proposed. Compared to the conventional ICA, the TVICA method allows the mixing matrix to be time dependent. Estimation is conducted under local homogeneity that assumes at any particular time point, there exists an interval over which the mixing matrix can be well approximated as constant. A sequential log likelihood-ratio testing procedure is used to automatically identify such local intervals. Numerical analysis demonstrates that TVICA provides good performance in homogeneous situations and does improve accuracy in nonstationary settings with possible structural change. In real data analysis with application to risk management, the TVICA confirms a superior performance when compared to several alternatives, including ICA, PCA and DCC-based models.