A novel seasonal grey prediction model with fractional order accumulation for energy forecasting

To accurately predict sequence data with seasonal characteristics, we combine data restart technology and fractional order accumulation into a novel seasonal grey model (FSGM (1,1, $$)). The particle swarm optimization (PSO) algorithm is used to solve the fractional order and background value coefficients of the model, and the effectiveness of FSGM (1,1, $$) is verified using three cases. Finally, we use FSGM (1,1, $$) to predict quarterly electricity generation in Beijing and Henan Province and quarterly petroleum coke production in China from 2023 to 2027. The research results indicate that, first, FSGM (1,1, $$) is reasonable and effective and has the ability to accurately capture the dynamic trend of seasonal data. Second, compared with the grey model (GM (1,1)), seasonal grey model (SGM (1,1)), data grouping grey model (DGGM (1,1)), data grouping seasonal model (DGSM (1,1)), and data grouping seasonal time model (DGSTM (1,1)), which have seasonal characteristics, FSGM (1,1, $$) can better fit the original data, achieve higher prediction accuracy, and perform better. Third, from 2023 to 2027, it is predicted that there will be no significant change in Beijing's electricity generation, and the current stable trend will be maintained. Both the power generation in Henan Province and the petroleum coke production in China will steadily increase to a certain extent, with obvious seasonal cyclical fluctuations. Notably, the power generation and petroleum coke production in Henan Province in the fourth quarter of 2027 will increase by 11.50 % and 10.93 %, respectively, compared to those in the fourth quarter of 2023.