Improving the forecasting accuracy of interval-valued carbon price from a novel multi-scale framework with outliers detection: An improved interval-valued time series analysis mode

Accurate carbon price forecasting can provide policymakers with a reasonable basis for carbon pricing. Interval -valued carbon price forecasting could provide sufficient information compared with real-valued carbon price time series prediction. On the other hand, current interval-valued carbon price forecasting has major challenges including data complexity, outliers, and the selection of forecasting methods, which make the forecasting results with great uncertainty and instability. To address these issues, this paper proposes an interval-valued carbon price forecasting method based on new data processing techniques, and discusses the effects of different com-binations of interval variables on the forecasting results. We first established interval complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and interval outlier detection method (I-ksigma) to reduce the data complexity and identify outliers. Then, various neural network models include in-terval multilayer perceptron (IMLP), multi-output support vector regression (MSVR), long short-term memory network (LSTM), gated recurrent unit neural network (GRU), and convolution neural network (CNN) are chosen to conduct combination forecasting on the interval sub-modes produced by ICEEMDAN. The final results are obtained by summing the interval sub-modes. Finally, taking the carbon trading price in Hubei as the research object, the results show that the developed forecasting framework is superior to all comparison models in forecasting precision and stability. Furthermore, different combinations of interval variables (CRM, Minmax, L + 2R, and U-2R) lead to different decomposition results and outlier detection results, which finally affect the prediction results.