Sliced Inverse Regression for High-dimensional Time Series

Methods of dimension reduction are very helpful and almost a necessity when analyzing high-dimensional time series since otherwise modelling affords many parameters because of interactions at various time-lags. We use a dynamic version of Sliced InverseRegression (SIR; (1991)) as an exploratory tool for analyzing multivariate time series. Analyzing each variable individually, wesearch for those directions, i.e, linear combinations of past and present observations of the other variables which explain most of its variability. This also provides information on possible nonlinearities. An application to time series representing the hemodynamic system is given.