Abstract
In order to further improve the prediction accuracy of the chaotic time series and overcome the defects of the single model, a multi-model hybrid model of chaotic time series is proposed. First, the Discrete Wavelet Transform (DWT) is used to decompose the data and obtain the approximate coefficients (low-frequency sequence) and detailed coefficients (high-frequency sequence) of the sequence. Secondly, phase space reconstruction is performed on the decomposed data. Thirdly, the chaotic characteristics of each sequence are judged by correlation integral and Kolmogorov entropy. Fourthly, in order to explore the deeper features of the time series and improve the prediction accuracy, a sequence of Volterra adaptive prediction models is established for the components with chaotic characteristics according to the different characteristics of each component. For the components without chaotic characteristics, a JGPC prediction model without chaotic feature sequences is established. Finally, the multi-model fusion prediction of the above multiple sequences is carried out by the LSTM algorithm, and the final prediction result is obtained through calculation, which further improves the prediction accuracy. Experiments show that the multi-model hybrid method of Volterra-JGPC-LSTM is more accurate than other comparable models in predicting chaotic time series.
Highlights
Chaotic time series are highly non-linear, uncertain and random, etc., and it is difficult to master the change rules and characteristics of conventional analysis and prediction methods, making it a difficult problem to make an accurate prediction of time series [1]
The evaluation index of predictability uses root means squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and determination coefficient R, and calculates the percentage reduction and increase of R in the Volterra-JGPC-Long short-term memory (LSTM) model and comparison model mentioned in this paper
Compared with the Volterra model in one-step, two-step, and three-step predictions, the RMSE of the Volterra-JGPC-LSTM model reduced by 20.33 %, 22.89 %, and 31.27 % respectively, and the MAE reduced by 31.21 %, 23.74 %, and 25.34 % respectively, MAPE reduced by 28.20 %, 26.39 %, and 19.55 % respectively, and R increased by 3.24 %, 4.20 %, and 4.59 % respectively
Summary
Chaotic time series are highly non-linear, uncertain and random, etc., and it is difficult to master the change rules and characteristics of conventional analysis and prediction methods, making it a difficult problem to make an accurate prediction of time series [1]. CHAOTIC TIME SERIES PREDICTION USING WAVELET TRANSFORM AND MULTI-MODEL HYBRID METHOD. Literature [13, 14] proposes a method of wavelet transform and multi-model fusion to predict time series. In the literature [15], the wavelet transform and the cyclic neural network model are used to decompose the watermark time series, and the decomposed data are separately modeled and predicted. In order to further improve the prediction accuracy of the chaotic time series, a hybrid Volterra-JGPC-LSTM model is proposed to predict the chaotic time series. When calculating the final predicted value, this paper does not directly accumulate the prediction of each part but uses the LSTM algorithm to perform multi-model fusion prediction on the above sequence. The combined prediction error is smaller than the single model prediction error, which further improves the prediction accuracy
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