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**Modelling the dynamics of nonlinear time series using canonical variate analysis.**
*(English)*
Zbl 1019.37046

Summary: We report on a novel prediction method of nonlinear time series based on canonical variate analysis (CVA) and radial basis modelling. Nonlinear models of possibly chaotic and noisy systems are constructed from data via a nonlinear CVA of the past and future of the process. The canonical variables give an optimal linear combination of nonlinear coordinates of the past for describing the future. We show how our method can be used for prediction, give a comparison with other methods, and apply our prediction algorithm to simulated data from the Lorenz system and the logistic map, to a laser experimental time series, and to sunspot data. The focus of this work is to obtain models that accurately reflect the dynamics of the system: A model should not only fit data and predict it well, but should also have a dynamical behaviour similar to that of the measured system. The results indicate that the algorithm presented is able to capture the dynamics of complex systems and gives reliable predictions when using only short data sets.

### MSC:

37M10 | Time series analysis of dynamical systems |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

### Keywords:

noisy systems; Lorenz system; logistic map; chaotic systems; nonlinear modelling; nonlinear prediction; radial basis modelling
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\textit{B. Pilgram} et al., Physica D 170, No. 2, 103--117 (2002; Zbl 1019.37046)

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