Abstract
The embedding dimension and the number of nearest neighbors are very important parameters in the prediction of a chaotic time series. In order to reduce the uncertainties in the determination of the forgoing two parameters, a new adaptive local linear prediction method is proposed in this study. In the new method, the embedding dimension and the number of nearest neighbors are combined as a parameter set and change adaptively in the process of prediction. The generalized degree of freedom is used to help select the optimal parameters. Real hydrological time series are taken to examine the performance of the new method. The prediction results indicate that the new method can choose the optimal parameters of embedding dimension and the nearest neighbor number adaptively in the prediction process. And the nonlinear hydrological time series perhaps could be modeled better by the new method.
Highlights
The global and regional climates have already begun changing 1, and meteorologicaldriven processes have been studied by some researchers just as the study in the signal analysis and other fields 2–8
In the selection of the optimal parameter set m, q for each prediction step, the generalized degrees of freedom GDF are used and different error variances are calculated under different combinations of m, q
The accuracy of prediction is evaluated by three measurement indices in this study, which are the Mean absolute error (MAE), Root mean square error (RMSE), and Correlation coefficient (CC)
Summary
The global and regional climates have already begun changing 1 , and meteorologicaldriven processes have been studied by some researchers just as the study in the signal analysis and other fields 2–8. Many hydrological processes, such as runoff, are usually nonlinear, complex, dynamic processes because of the involved physical process and the considerable spatial and temporal variability 9. The emergence of chaos theory provides a new way to study this kind of highly complex system and makes it possible to extract deterministic regulation from the seemingly disordered hydrological phenomenon. A series of theories and methods identifying chaotic essences
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