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We generalize the concept of local states (LS) for the prediction ofhigh-dimensional, potentially mixed chaotic systems. The construction ofgeneralized local states (GLS) relies on defining distances between time serieson the basis of their (non-)linear correlations. We demonstrate the predictioncapabilities of our approach based on the reservoir computing (RC) paradigmusing the Kuramoto-Sivashinsky (KS), the Lorenz-96 (L96) and a combination ofboth systems. In the mixed system a separation of the time series belonging tothe two different systems is made possible with GLS. More importantly,prediction remains possible with GLS, where the LS approach must naturallyfail. Applications for the prediction of very heterogeneous time series withGLSs are briefly outlined.

Predicting high-dimensional heterogeneous time series employing generalized local states