A novel structured discrete grey Gompertz multivariable prediction model and its application

In this study, a conformable Hausdorff accumulation generation operation is designed, and the grey Gompertz model is extended to a multivariable form. Additionally, a time power term is introduced as the grey action quantity in the model. Finally, through discretization, a novel structured discrete grey Gompertz multivariable prediction model is constructed. By incorporating the Gompertz function into the multivariable grey prediction model and adopting a more flexible accumulation generation operation, the proposed model enhances its adaptability, thereby improving its predictive capability. Furthermore, the Particle Swarm Optimization algorithm is employed to optimize the hyperparameters within the model. To validate the effectiveness of the model,the proposed framework is compared with six multivariable grey prediction models and four machine learning prediction methods in forecasting China’s annual energy consumption and total retail sales of consumer goods. Multiple evaluation metrics are used to comprehensively assess the predictive performance of each model. Experimental results demonstrate that the proposed model outperforms all competing algorithms across all evaluation indicators, further confirming its effectiveness.