A nonlinear interactive grey multivariable model based on dynamic compensation for forecasting the economy-energy-environment system

Achieving the goals of emissions intensity reduction and energy structure transformation while ensuring stable economic development is essential for sustainable development in China. Establishing a concise and accurate model for predicting the 3E (economy-energy-environment) system is beneficial for decision-makers in devel-oping optimal long-term energy and environmental planning. Although previous studies have concentrated on the interaction of variables in the 3E system, frameworks for prediction have thus far been limited. In this paper, we develop a novel nonlinear interactive grey multivariable model based on dynamic compensation, denoted as DCNIGM(1, N), to perform the prediction of the 3E system. More specifically, the proposed model innovatively takes into account nonlinear driving effects to elucidate nonlinear interactive relationships between the system variables. A dynamic compensation mechanism is introduced into the systematic grey modeling for the first time to adapt to a dynamic system. In addition, the Whale Optimization Algorithm (WOA) is employed to determine the optimal nonlinear parameters to improve the forecast accuracy. To evaluate the performance of the DCNIGM(1, N) model in forecasting the 3E system, two existing grey forecasting models, three statistical ap-proaches, and three machine learning models are selected as the benchmark models. Moreover, two more cases with different variables of the 3E system are applied to verify the feasibility and effectiveness of the proposed model. Experimental results indicate that the DCNIGM(1, N) model possesses the most excellent performance in all cases, showing the effectiveness and generalizability of the proposed method. The prediction from 2019 to 2020 shows that carbon emissions, total energy consumption, and gross domestic product will grow steadily.