2010/12/17 by Manuel D. de la Iglesia, Esteban G. Tabak, de la Iglesia, Manuel D. +1
Computer Science · Earth and Planetary Sciences · Environmental Science · Mathematics · #37M10 #62H25 #62M10 #Climate variability and models #FOS: Mathematics #Oceanographic and Atmospheric Processes #Statistics Theory (math.ST) #Time Series Analysis and Forecasting #math.ST #msc:37M10 #msc:62H25 #msc:62M10 #stat.TH
paper · pdf · doi:10.48550/arxiv.1012.3963
29 pages, 14 figures
arxiv created 2010/12/17 · openalex publication_date 2010/12/17 · arxiv updated 2010/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.