Accurate prediction of the carbon trading price (CTP) is crucial to the decision-making of relevant stakeholders, and can also provide a reference for policy makers. However, the time interval for the CTP is one day, resulting in a relatively small sample size of data available for predictions. When dealing with small sample data, deep learning algorithms can trade only a small improvement in prediction accuracy at the expense of efficiency and computing time. In contrast, fine-grained configurations of traditional model inputs and parameters often perform no less well than deep learning algorithms. In this context, this paper proposes a novel hybrid CTP prediction model based on the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and a windowed-based XGBoost approach. First, the initial CTP data is decomposed into multiple subsequences with relatively low volatility and randomness based on the CEEMDAN algorithm. Then, the decomposed carbon valence series and covariates are subject to windowed processing to become the inputs of the XGBoost model. Finally, the universality of the proposed model is verified through case studies of four carbon emission trading markets with different modal characteristics, and the superiority of the proposed model is verified by comparing with seven other models. The results show that the prediction error of the proposed XGBoost(W-b) algorithm is reduced by 4.72%~81.47% compared to other prediction algorithms. In addition, the introduction of CEEMDAN further reduces the prediction error by 25.24%~89.28% on the basis of XGBoost(W-b).

With the continuous development of new power systems, the load demand on the user side is becoming more and more diverse and random, which also brings difficulties in the accurate prediction of power load. Although the introduction of deep learning algorithms has improved the prediction accuracy to a certain extent, it also faces problems such as large data requirements and low computing efficiency. An ultra-short-term load forecasting method based on the windowed XGBoost model is proposed, which not only reduces the complexity of the model, but also helps the model to capture the autocorrelation effect of the forecast object. At the same time, the real-time electricity price is introduced into the model to improve its forecast accuracy. By simulating the load data of Singapore’s electricity market, it is proved that the proposed model has fewer errors than other deep learning algorithms, and the introduction of the real-time electricity price helps to improve the prediction accuracy of the model. Furthermore, the broad applicability of the proposed method is verified by a sensitivity analysis on data with different sample sizes.