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In recent years, the grey-based models with fractional accumulation have received extensive attention by scholars and have been widely used in various fields. However, the existing rough construction of the background value in the fractional grey model impairs its predictive performance to some extent. To address this problem, this paper reconstructs a dynamic background value for the fractional grey model by the composite integral median theorem, as a result, a novel fractional grey model-based variable background value (denoted as OFAGM(1,1) for short) is proposed. In particular, the Particle Swarm Optimization algorithm (PSO) is then employed to determine the optimum for the fractional order and the background value coefficients. Based on electricity consumption of two regions of China (i.e. Beijing, Inner Mongolia), the superiority of the proposed model has been verified in comparison with other benchmark models, the electricity consumption of Beijing is predicted to reach [Formula: see text][Formula: see text]Kwh in 2022 and that of Inner Mongolia will reach [Formula: see text][Formula: see text]Kwh in 2023. This study also takes the relative growth rate and the doubling time into account for these two regions that facilities comparison of the regions’ performance.
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