Principal Dynamical Components

Manuel D. de la Iglesia, Esteban Tabak

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)48-82
Number of pages35
JournalCommunications on Pure and Applied Mathematics
Volume66
Issue number1
DOIs
StatePublished - Jan 2013

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Principal Components
Dynamical Model
Time series
Sea Surface Temperature
Information Loss
Predictive Model
Dimension Reduction
Minimise
Uncertainty
Scenarios
Interaction
Temperature

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Principal Dynamical Components. / de la Iglesia, Manuel D.; Tabak, Esteban.

In: Communications on Pure and Applied Mathematics, Vol. 66, No. 1, 01.2013, p. 48-82.

Research output: Contribution to journalArticle

de la Iglesia, Manuel D. ; Tabak, Esteban. / Principal Dynamical Components. In: Communications on Pure and Applied Mathematics. 2013 ; Vol. 66, No. 1. pp. 48-82.
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