We consider multivariate time series where each component series is an unknown linear combination of latent mutually independent stationary time series. Multivariate financial time series have often periods of low volatility followed by periods of high volatility. This kind of time series have typically non-Gaussian stationary distributions, and therefore standard independent component analysis (ICA) tools such as fastICA can be used to extract independent component series even though they do not utilize any information on temporal dependence. In this paper we review some ICA methods used in the context of stochastic volatility models. We also suggest their modifications which use nonlinear autocorrelations to extract independent components. Different estimates are then compared in a simulation study.