Abstract: Energy consumption consistently exhibits pronounced non-linearity, making trend prediction difficult when only limited samples are available. To overcome this challenge, we employ Laguerre polynomials to construct a novel grey forecasting model that integrates fractional difference and accumulation. Empirical results show that the proposed model outperforms alternative approaches in accuracy, stability, and applicability. The proposed model, optimized via particle swarm optimization, manifested superior forecasting precision for energy consumption in Heilongjiang, Jiangsu, and Xinjiang, with mean absolute percentage error values of 5.225%, 4.098%, and 4.392% respectively. This performance conspicuously surpassed five traditional grey system models and two machine learning models, accentuating the robustness and exactitude of the model in capturing regional crude oil consumption patterns and trends. Furthermore, the newly proposed model was applied to a representative set of major oil-consuming economies, and, for every country considered, the out-of-sample forecasts remained below 10% error, underscoring the model’s robustness and its practical utility for global energy-demand planning.

Key words: Fractional grey model, Polynomial grey system, Intelligent optimization algorithm, Energy consumption forecasting