The carbon market is recognized as the most effective means for reducing global carbon dioxide emissions. Effective carbon price forecasting can help the carbon market to solve environmental problems at a lower economic cost. However, the existing studies focus on the carbon premium explanation from the perspective of return and volatility spillover under the framework of the mean-variance low-order moment. Specifically, the time-varying, high-order moment shock of market asymmetry and extreme policies on carbon price have been ignored. The innovation of this paper is constructing a new hybrid model, NAGARCHSK-GRU, that is consistent with the special characteristics of the carbon market. In the proposed model, the NAGARCHSK model is designed to extract the time-varying, high-order moment parameter characteristics of carbon price, and the multilayer GRU model is used to train the obtained time-varying parameter and improve the forecasting accuracy. The results conclude that the NAGARCHSK-GRU model has better accuracy and robustness for forecasting carbon price. Moreover, the long-term forecasting performance has been proved. This conclusion proves the rationality of incorporating the time-varying impact of asymmetric information and extreme factors into the forecasting model, and contributes to a powerful reference for investors to formulate investment strategies and assist a reduction in carbon emissions.

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Global carbon dioxide emissions have become a great threat to economic sustainability and human health. The carbon market is recognized as the most promising mean to curb carbon emissions, furthermore, carbon price forecasting will promote the role of the carbon market in emissions reduction and achieve reduction targets at lower economic costs for emission entities. However, there are still some technical problems in carbon price prediction, such as mode mixing and larger reconstruction error for the traditional empirical mode decomposition-type models. Therefore, the innovation of this paper is constructing a novel carbon price prediction model of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)-long short-term memory (LSTM), that combines the advantages of CEEMDAN in decomposing the multiscale time-frequency carbon price signals and the LSTM model in fitting the financial signals. The results show the proposed CEEMDAN-LSTM model has significant accuracy in predicting the complex carbon price signals. The prediction error and expectation indicators of root mean square error, mean absolute error, mean absolute percentage error, and direction accuracy are 0.638342, 0.448695, 0.015666, and 0.687631, respectively, which is better than other benchmark models. Further evidence convince that the short-term forecasting performance is superior to the long-term and medium-term performance. That evidence concludes that the proposed model is a reliable method to reveal the carbon price-driving mechanism from the point of multiscale time-frequency characteristics. Particularly, short-term forecasting is more accurate and can provide a valuable technical reference for reduction entities and green financial companies to judge the market situation and formulate quantitative transactions.

Predicting the carbon price accurately can not only promote the sustainability of the carbon market and the price driving mechanism of carbon emissions, but can also help investors avoid market risks and increase returns. However, previous research has only focused on the low-order moment perspective of the returns for predicting the carbon price, while ignoring the shock of extreme events and market asymmetry originating from its pricing factor markets. In this paper, a novel extended higher-order moment multi-factor framework (EHM-APT) was formed to improve the prediction and to capture the driving mechanism of the carbon price. Furthermore, a multi-layer and multi-variable Long Short-Term Memory Network (Multi-LSTM) model was constructed so that the parameters and structure could be determined experimentally for testing the performance of the proposed framework. The results show that the pricing framework considers the shock of extreme events and market asymmetry and can improve the prediction compared with a framework that does not consider the shock of higher-order moment terms. Additionally, the Multi-LSTM model is more competitive for prediction than other benchmark models. This conclusion proves the rationality and accuracy of the proposed framework. The application of the pricing framework encourages investors and financial institutions to pay more attention to the pricing factor of extreme events and market asymmetry for accurate price prediction and investment analysis.

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