Forecasting fossil fuel consumption and greenhouse gas emissions using novel multi-variable grey system model with convolution integrals

Economic development, population growth and the use of fossil fuels significantly impact global carbon emissions, exacerbating global warming and environmental pollution. Therefore, predicting fossil fuel consumption and greenhouse gas emissions is crucial. This work integrates the characteristics of the multi-output multi-variable grey model and the grey model with convolution integral to establish a multi-variable grey system model with convolution integrals. Using two sets of real-world data, this work forecasts fossil fuel consumption and greenhouse gas emissions. Each case is analyzed from three different perspectives by employing varying numbers of system characteristic variables. The experimental results show that the proposed model demonstrates excellent predictive performance, with errors consistently lower than those of benchmark models. It effectively balances the accuracy of data fitting with the stability of predictions. In the prediction of fossil energy consumption and greenhouse gas emissions, during the model prediction phase, France’s lowest Mean Absolute Percentage Error can reach 3.9391%, and Germany’s is at 2.7996%. Moreover, compared to benchmark models, the proposed model achieves the highest accuracy improvements of 97.4678% in one case and 97.8835% in the other, highlighting its capability to balance data fitting accuracy and prediction stability.