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Principal dynamical components
Manuel D. de la Iglesia, Esteban G. Tabak · 2010-12-18 · via math.ST updates on arXiv.org

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.

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