Paying attention to distortion: improving the accuracy of multistep-ahead carbon price forecasting with shape and temporal criteria

Accurate multistep-ahead carbon price forecasting is crucial for ensuring the smooth operation of the carbon market, as it provides policy-makers with invaluable insights into future price trends. However, current state-of-the-art carbon price forecasting models, which are trained primarily via the mean squared error loss function, struggle to deliver precise and timely forecasts. To bridge this gap, this study introduces a hybrid multistep-ahead carbon price forecasting model that incorporates a training objective that encompasses both shape and temporal criteria. Specifically, this training objective includes two components: one aimed at accurate shape detection, which effectively captures the overall pattern of price movements, and the other focused on temporal variation identification, which excels in capturing changes over time. By integrating these components, the proposed model significantly reduces the loss associated with time delays while also improving forecasting shape coincidence. To validate the superiority of the proposed model, three-step-ahead, four-step-ahead, and five-step-ahead forecasting were conducted on two datasets from the European Union Emissions Trading System. The results show that the proposed model possesses a remarkable ability to capture abrupt changes in nonstationary carbon price data and achieves superior forecasting accuracy compared with other benchmark models, thus demonstrating its potential for practical applications in the carbon markets.