A novel grey fractional model based on model averaging for forecasting time series

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.