A novel dynamic grey multivariate prediction model for multiple cumulative time-delay shock effects and its application in energy emission forecasting

Energy emission systems are often influenced by external information and policy shock. However, conventional grey models ignore the existence of the impact of multiple shock events and cumulative time -delay effects, which are crucial for achieving accurate forecasts. From a dynamic perspective, we aim to establish a multivariable grey prediction model considering the impact of multiple shock events, namely MSGTDM(1,N) model. Specifically, to accurately describe the impact of different types of external shocks on the system, three kinds of nonlinear dynamic shock functions are designed, including growth dynamic shock function, decline dynamic shock function, and slope dynamic shock function. Based on this, multi -dimensional instantaneous shock utility terms and cumulative time -delay utility terms are constructed to accurately measure shock effects. And Whale Optimization Algorithm is employed to determine the optimal parameters of the shock functions through comprehensive comparative analysis. The findings affirm the MSGTDM(1,N) model ' s higher predictive accuracy and validity. Consequently, the forecast results of China ' s carbon emissions from coal and natural gas consumption in 2022 - 2025 provide a reliable basis for adjusting the energy structure and implementing the " dual -carbon " policy effectively.