Causal neural network for carbon prices probabilistic forecasting

A precise understanding of carbon price dynamics is critical for the stable operation of carbon trading markets and the achievement of emission reduction targets. While prior research has mainly focused on point and interval predictions of carbon prices, probabilistic forecasting has received comparatively little attention. Moreover, the “black-box” neural networks often excel in prediction accuracy, but generally overlook the underlying causal dynamics in carbon trading markets. To address these limitations, we propose a carbon price probabilistic forecasting model based on ensemble probability patch transform (EPPT) and monotonic composite quantile causal temporal convolutional networks (MCQCTCN). First, EPPT extracts carbon price trend features at various probability levels. Subsequently, key factors influencing carbon prices, identified through the Granger causality test, are used as input variables for model training, allowing the MCQCTCN model to generate accurate composite quantile predictions. Finally, non-parametric kernel density estimation (KDE) is applied to derive daily conditional probability distributions, providing a comprehensive representation of potential carbon price fluctuations. Compared to baseline models, experimental results on Guangdong and European Union allowances confirm the superiority of the proposed model, with average weighted quantile score values decreasing by 83 % and 80 %, and root mean square error decreasing by 27 % and 61 % for the respective regions. The value of mean absolute percentage error reaches 0.4 % and 0.2 %. It reveals the relationships between influencing factors and carbon prices, offering policymakers and businesses deeper insights to support informed decision-making and promoting the sustainable operation of carbon trading markets.