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Regularized local linear prediction of chaotic time series. (English) Zbl 0931.37037

Summary: Local linear prediction, based on the ordinary least squares (OLS) approach, is one of several methods that have been applied to prediction of chaotic time series. Apart from potential linearization errors, a drawback of this approach is the high variance of the predictions under certain conditions. Here, a different set of so-called linear regularization techniques, originally derived to solve ill-posed regression problems, are compared to OLS for chaotic time series corrupted by additive measurement noise. These methods reduce the variance compared to OLS, but introduce more bias. A main tool of analysis is the singular value decomposition (SVD), and a key to successful regularization is to damp the higher order SVD components. Several of the methods achieve improved prediction compared to OLS for synthetic noise-corrupted data from well-known chaotic systems. Similar results were found for real-world data from the R-R intervals of ECG signals. Good results are also obtained for real sunspot data, compared to published predictions using nonlinear techniques.

MSC:

37M10 Time series analysis of dynamical systems
62M20 Inference from stochastic processes and prediction
93C99 Model systems in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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