Sliced inverse regression for high-dimensional time series

Methods of dimension reduction are very helpful and almost a necessity if we want to analyze high-dimensional time series since otherwise modelling affords many parameters because of interactions at various time-lags. We use a dynamic version of Sliced Inverse Regression (SIR; Li (1991)), which was developed to reduce the dimension of the regressor in regression problems, as an exploratory tool for analyzing multivariate time series. Analyzing each variable individually, we search for those directions, i.e., linear combinations of past and present observations of the other variables which explain most of the variability of the variable considered. This can also provide information on possible nonlinearities. We apply a dynamic version of SIR to multivariate physiological time series observed in intensive care.