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Two recent papers on prediction of chaotic systems, one on multi-viewembedding1 , and the second on prediction in projection2 provide empiricalevidence to support particular prediction methods for chaotic systems.Multi-view embedding1 is a method of using several multivariate time series tocome up with an improved embedding based predictor of a chaotic time series.Prediction in projection2 discusses how much smaller embeddings can provideuseful prediction even though they may not be able to resolve the dynamics ofthe system. Both papers invoke a nearest neighbor3, or Lorenz method ofAnalogue (LMA)4 approach to estimation. However with open high dimensionalchaotic systems there may be no very close nearest neighbor trajectories in ahistory, so in this paper we add in the thread of linear response theory5,although our approach is quite simple assuming that linear regressions6 onmultiple embeddings5 will be sufficient. The approach is thus to create linearresponse models5 of multiple1 low dimensional embeddings2 to provide practicalmethods of predicting in high dimensional, open chaotic systems. Some theory isdeveloped, mostly around two unproven conjectures to suggest methods ofprediction, and they are applied to prediction in the earth's climate system(predicting regional rainfall in a small region) multiple seasons ahead and topower a simulated automated trading program applied to three stock indexes, theDow Jones industrial average, the Dow Jones transportation average, and the DowJones utility average, based on data from 1929 through 20077

A simple statistical approach to prediction in open high dimensional chaotic systems