  In the independent component model, the multivariate data is assumed to be a
mixture of mutually independent latent components, and in independent component
analysis (ICA) the aim is to estimate these latent components. In this paper we
study an ICA method which combines the use of linear and quadratic
autocorrelations in order to enable efficient estimation of various kinds of
stationary time series. Statistical properties of the estimator are studied by
finding its limiting distribution under general conditions, and the asymptotic
variances are derived in the case of ARMA-GARCH model. We use the asymptotic
results and a finite sample simulation study to compare different choices of a
weight coefficient. As it is often of interest to identify all those components
which exhibit stochastic volatility features we also suggest a test statistic
for this problem. We also show that a slightly modified version of principal
volatility components (PVC) can be seen as an ICA method. Finally, we apply the
estimators in analyzing a data set which consists of time series of exchange
rates of seven currencies to US dollar. Supplementary material including proofs
of the theorems is available online.
