  A new 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 new 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.
Further generalizations are provided to non-autonomous and non-Markovian
scenarios, which are then applied to historical sea-surface temperature data.
