Principal Dynamical Components

A procedure is proposed for a dimension reduction in 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 nonautonomous and non-Markovian scenarios, which are then applied to historical sea-surface temperature data.