Affiliations: [a]
School of Sciences, Guangxi University of Science and Technology, Liuzhou, China
| [b]
Tus College of Digit, Guangxi University of Science and Technology, Liuzhou, China
| [c]
School of Mathematical Sciences, Jiangsu University, Zhenjiang, China
Correspondence:
[*]
Corresponding authors. Tao Zhang, Tus College of Digit, Guangxi University of Science and Technology, Liuzhou 545006, China. E-mail: taozhangmaths@gxust.edu.cn and Wen-Ze Wu, School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China. E-mail: bsstatistics@126.com.
Abstract: The introduction of fractional order accumulation has played a crucial role in the development of grey forecasting methods. However, accurately identifying a single fractional order accumulation for modeling diverse sequences is challenging due to the dependence of different fractional order accumulations on data structure over time. To address this issue, we propose a novel fractional grey model abbreviated as FGMMA, incorporating a model averaging method. The new model combines existing fractional grey models by using four judgment criteria, including Akaike information criteria, Bayesian information criteria, Mallows criteria, and Jackknife criteria. Meanwhile, the cutting-edge algorithm named breed particle swarm optimization is employed to search the optimal fractional order for each candidate model to enhance the effectiveness of the designed model. Subsequently, we conduct a Monte Carlo simulation for verification and validation purposes. Finally, empirical analysis based on energy consumption in three countries is conducted to verify the applicability of the proposed model. Compared with other benchmark models, we can conclude that the proposed model outperforms the other competitive models.
Keywords: Grey forecasting model, fractional order accumulation, model averaging, breed particle swarm optimization
