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Improved Multi-Scale Deep Integration Paradigm for Point and Interval Carbon Trading Price Forecasting


  • Jujie Wang

    (School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
    Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China)

  • Shiyao Qiu

    (School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China)


The forecast of carbon trading price is crucial to both sellers and purchasers; multi-scale integration models have been used widely in this process. However, these multi-scale models ignore the feature reconstruction process as well as the residual part and also they often focus on the linear integration. Meanwhile, most of the models cannot provide prediction interval which means they neglect the uncertainty. In this paper, an improved multi-scale nonlinear integration model is proposed. The original dataset is divided into some subgroups through variational mode decomposition (VMD) and all the subgroups will go through sample entropy (SE) process to reconstruct the features. Then, random forest and long-short term memory (LSTM) integration are used to model feature sub-sequences. For the residual part, LSTM residual correction strategy based on white noise test corrects residuals to obtain point prediction results. Finally, Gaussian process (GP) is applied to get the prediction interval estimate. The result shows that compared with some other methods, the proposed method can obtain satisfying accuracy which has the minimum statistical error. So, it is safe to conclude that the proposed method is able to efficiently predict the carbon price as well as to provide the prediction interval estimate.

Suggested Citation

  • Jujie Wang & Shiyao Qiu, 2021. "Improved Multi-Scale Deep Integration Paradigm for Point and Interval Carbon Trading Price Forecasting," Mathematics, MDPI, vol. 9(20), pages 1-20, October.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2595-:d:657234

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