Proceedings PaperBest judge of closeness of delay vectors in embedding space? The Euclidean metric...not!
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An improved method for forecasting a time series is demonstrated. Forecasts are based on future behavior of nearest neighbors in an embedding space of time delay vectors. The metric of this space is generalized, rather than Euclidean. Reduction of forecast error and high probability of improved forecast are demonstrated for various chaotic time series. The approach also works for chaotic time series with added measurement noise. In addition, a lower bound on forecast error is calculated.