Carbon trading price prediction with spikes: A novel hybrid model framework using heuristic multi-head attention convolutional bidirectional recurrent neural network

Accurate forecasting of carbon trading prices (CTPs) with spikes is crucial for developing carbon emission reduction policies and planning corporate investments. However, most existing CTP approaches usually focus on designing a cutting-edge model without considering spike prediction. Therefore, this paper presents a novel heuristic optimization-based hybrid model framework for CTP prediction with spikes. First, random forest is exploited to identify the relevant features of spikes and non-spikes for CTPs, and categorical boosting is employed to predict the spike occurrences of CTPs. Then, a novel hybrid model based on multiple linear regression, categorical boosting, and two dimensions convolutional neural network and bidirectional gated recurrent unit with multi-head regularized attention mechanism (2DCNN-BiGRU-MRA) is proposed to predict spikes and non-spikes for CTPs. In this model, multiple linear regression and categorical boosting are respectively applied to capture the linear and complex nonlinear features of the CTPs, in which their prediction results and deviations are integrated into the 2DCNN-BiGRU-MRA model as relevant features. The proposed 2DCNN-BiGRU-MRA can learn the spatiotemporal features and enhance representation capabilities by introducing 2DCNN, BiGRU, and MRA, thereby improving the accuracy of CTP prediction. In addition, to construct appropriate model hyperparameters of 2DCNN-BiGRU-MRA, the strength honey badger algorithm based on the adaptive momentum estimation is proposed to optimize the hyperparameters of 2DCNN-BiGRU-MRA. Finally, the proposed framework is tested on the actual data of European Union emissions trading and the carbon market in Hubei, China, and case studies have confirmed the superiority and achievable local interpretability of the proposed hybrid model framework.