Principal dynamical components

A procedure is proposed for the dimensional reduction of time series. Similarly to principal components, the procedure seeks a low-dimensional manifold that minimizes information loss. Unlike principal components, however, the procedure involves dynamical considerations, through the proposal of a predictive dynamical model in the reduced manifold. Hence the minimization of the uncertainty is not only over the choice of a reduced manifold, as in principal components, but also over the parameters of the dynamical model, as in autoregressive analysis and principal interaction patterns. Further generalizations are provided to non-autonomous and non-Markovian scenarios, which are then applied to historical sea-surface temperature data. c © 2000 Wiley Periodicals, Inc.