Supervised dimension reduction for multivariate time series

A regression model where the response as well as the explaining variables are time series is considered. A general model which allows supervised dimension reduction in this context is suggested without considering the form of dependence. The method for this purpose combines ideas from sliced inverse regression (SIR) and blind source separation methods to obtain linear combinations of the explaining time series which are ordered according to their relevance with respect to the response. The method gives also an indication of which lags of the linear combinations are of importance. The method is demonstrated using simulations and a real data example.