A Novel Extended Higher-Order Moment Multi-Factor Framework for Forecasting the Carbon Price: Testing on the Multilayer Long Short-Term Memory Network

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.