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Assuming homogeneity of the underlying dynamics, we construct delay coordinates of local states and then further reduce their dimensionality through Principle Component Analysis. The prediction uses nearest neighbour methods in the space of dimension reduced states to either cross-estimate or iteratively predict the future of a given frame. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio\u2013Cherry\u2013Fenton model, and the Kuramoto\u2013Sivashinsky model.\n<\/jats:p>","DOI":"10.1007\/s00332-019-09588-7","type":"journal-article","created":{"date-parts":[[2019,10,26]],"date-time":"2019-10-26T01:02:29Z","timestamp":1572051749000},"page":"713-735","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Predicting Spatio-temporal Time Series Using Dimension Reduced Local States"],"prefix":"10.1007","volume":"30","author":[{"given":"Jonas","family":"Isensee","sequence":"first","affiliation":[]},{"given":"George","family":"Datseris","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3058-1435","authenticated-orcid":false,"given":"Ulrich","family":"Parlitz","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,10,26]]},"reference":[{"key":"9588_CR1","doi-asserted-by":"publisher","unstructured":"Abarbanel, H.D.I.: Analysis of Observed Chaotic Data. 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