Abstract
Precise carbon price forecasting matters a lot for both regulators and investors. The improvement of carbon price forecasting can not only provide investors with rational advice but also make for energy conservation and emission reduction. But traditional methods do not perform well in prediction because of the nonlinearity and non-stationarity of carbon price. In this study, an innovative multiscale nonlinear integration model is proposed to improve the accuracy of carbon price forecasting, which combines optimal feature reconstruction and biphasic deep learning. For one thing, the optimal feature reconstruction, including variational mode decomposition (VMD) and sample entropy (SE), is used to extract different features from the original carbon price effectively. For another thing, biphasic deep learning based on deep recurrent neural network (DRNN) and gate recurrent unit (GRU) is applied to predict carbon price. DRNN, a novel framework of deep learning, is applied to predict each component. Meanwhile, GRU is used for nonlinear integration, and the final prediction of carbon price can be acquired through this procedure. For illustration and comparison, this study takes carbon price from Beijing, Hubei, and Shanghai in China as sample data to examine the capability of the proposed model. The empirical result proves that the new hybrid model can improve the carbon price predictive accuracy in consideration of statistical measurement. Hence, the novel hybrid model can be considered as an efficient way of predicting carbon prices.
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Data availability
The datasets analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
- ARIMA:
-
Autoregressive integrated moving average
- EMD:
-
Empirical mode decomposition
- EEMD:
-
Ensemble empirical mode decomposition
- DRNN:
-
Deep recurrent neural network
- ANN:
-
Artificial neural network
- GRU:
-
Gate recurrent unit
- BDS test:
-
Brock-Decher-Scheikman test
- AE:
-
Approximate entropy
- BP:
-
Back propagation
- GARCH:
-
Generalized autoregressive conditional heteroskedasticity
- GJR:
-
Gap junction remodeling
- WT:
-
Wavelet transform
- LSTM:
-
Long short-term memory
- MAE:
-
Mean absolute error
- MAPE:
-
Mean absolute percentage error
- RNN:
-
Recurrent neural network
- RMSE:
-
Root mean squared error
- SE:
-
Sample entropy
- ADF test:
-
Augmented Dickey-Fuller test
- VMD:
-
Variational mode decomposition
- GA:
-
Genetic algorithm
- SVM:
-
Support vector machine
- LSSVM:
-
Least square support vector machine
- XGBoost:
-
eXtreme gradient boosting
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (Grant No. 71971122 and 71501101).
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Jujie Wang, Qian Cheng, and Xin Sun: conceived of the presented idea, developed the theory and performed the computations, discussed the results, wrote the paper, and approved the final manuscript. All authors read and approved the final manuscript.
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Wang, J., Cheng, Q. & Sun, X. Carbon price forecasting using multiscale nonlinear integration model coupled optimal feature reconstruction with biphasic deep learning. Environ Sci Pollut Res 29, 85988–86004 (2022). https://doi.org/10.1007/s11356-021-16089-2
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DOI: https://doi.org/10.1007/s11356-021-16089-2