关键词: 碳价预测, 深度学习, 变分模态分解, BiLSTM, 注意力机制

Abstract: Recently, a global consensus has been reached that carbon emissions should be reduced in response to global environmental problems. It is now widely believed that an effective carbon tax policy and the establishment of a carbon emission trading system are the key to the transition to a low-carbon economy. Carbon prices, which directly mirror the supply and demand for carbon emission rights in carbon markets, exert significant influence over both investors and regulatory authorities. Accurate forecasts of carbon prices are essential for informed decision-making. However, carbon prices are affected by internal market mechanisms and external environmental fluctuations, and are therefore non-stationary and non-linear. Therefore, carbon price prediction faces a huge challenge. This paper improves the accuracy of carbon price prediction by complementing current research on the application of decomposition-forecast-ensemble hybrid models.
Currently, carbon price prediction models are shifting from traditional models to data-driven ones, enabling deep learning algorithms to have more applications in this field. To build an effective hybrid forecasting model and reduce data noise, the paper proposes a new framework that is based on the GA-VMD-CNN-BiLSTM-Attention hybrid model. Here the genetic algorithm (GA) is adopted to search the optimal parameter combination of variational mode decomposition (VMD); convolutional neural networks (CNN) are established to discover the relationship between influencing factors and carbon prices; a bidirectional long and short-term memory network (BiLSTM) is applied to extract time series information; and an attention mechanism is used to strengthen the influence of important information on carbon prices. In addition to deterministic point prediction, this paper uses a non-parametric kernel density estimation with Gaussian kernel function (KDE-Gaussian) for interval forecasting. The interval forecasting can quantify the uncertainty of carbon prices and serve as a more practical reference for decision-makers. In our empirical analysis, this paper uses data from China's Hubei Emission Exchange dating from April 2, 2014, to June 15, 2022, for a total of 1857 trading days, to predict the daily closing price. The four main innovations and contributions of this paper are as follows. First, GA-VMD is applied to obtain multiple intrinsic mode function (IMF) components, so as to input multiple effective and smooth subsequences in the forecasting model. The optimal parameters of VMD are found through continuous iteration of GA, which avoids the uncertainty of artificial selection and effectively eliminates the noise influence in the decomposition process. Second, a hybrid CNN-BiLSTM-Attention prediction model is established. The CNN feature extraction capability is combined with the BiLSTM time series information extraction capability to improve the one-way transmission LSTM into BiLSTM with simultaneous forward and backward transmission, thus enhancing the memory of the neural network. Third, an attention mechanism is introduced into the BiLSTM side. This method trains weights on the hidden states of all BiLSTM time steps. Consequently, it outputs all forecasting information by weighted summation. Therefore, it can improve the forecasting effect by increasing the influence of important information. Fourth, on the basis of deterministic point prediction, non-parametric KDE-Gaussian is applied for interval forecasting. The prediction intervals at different confidence levels can serve as an improved practical reference for decision-makers.
To verify the superiority of the proposed model, this paper presents a comparative analysis of 12 models divided into 3 groups. The first group includes the models of LSTM, BiLSTM, BiLSTM-Attention, and CNN-BiLSTM-Attention. In the second group, VMD is added to the benchmark models to reflect the effect of noise reduction. Then the genetic algorithm is added to the third group. We then evaluate the forecasting results of different models and compare them using point prediction evaluation metrics. Compared to 11 other models, the GA-VMD-CNN-BiLSTM-Attention model is more accurate and reliable: its goodness-of-fit (R²) reaches 98.91%, while its MAE, RMSE, and MAPE values are as low as 0.1246, 0.7298, and 0.0111, respectively. In addition to deterministic point prediction, the paper performs interval forecasting for 278 data points from the Hubei Emission Exchange in the test set to quantify the uncertainty of carbon prices and provide a more practical reference for decision-makers. The result shows that the KDE (Gaussian) prediction method provides a more reliable interval prediction, with a 15.57% reduction over the KDE (Epanechnikov) method and a 34.92% reduction over normal distribution in coverage width-based criterion (CWC) index at a 95% confidence level.
By revealing the particularly challenging issue that underlies carbon price forecasting, our analysis sheds light on current low-carbon policies in China. To improve these policies, the paper proposes that China should establish a comprehensive carbon emissions data system, gradually implement paid allocation of allowances, enrich trading products, and promote a jointly developed financial market and the carbon market. This paper has not yet considered how and to what extent other factors such as policy making and changes in domestic andinternational situations affect carbon prices. This is a possible direction for future studies.

Key words: carbon price prediction, deep learning, variational mode decomposition, BiLSTM, attention mechanisms