A novel self-adaptive fractional grey Euler model with dynamic accumulation order and its application in energy production prediction of China

Abstract

In the fractional grey model, the new information priority principle has always been pursued by researchers. However, it does not mean that new information is the most important, because in reality, there are always some special moments, and the information they represent will profoundly affect the future development. That is, the most important data may be in the middle of the sequence, not the latest data. Therefore, this paper proposes a periodic variable order accumulated generating operation, which can switch the priority of new and old information with time. In terms of model structure, this paper presents a new variable coefficient whitening equation with self-adaptive structure. That is, a new fractional order grey Euler model with dynamic accumulation order (DOFGM(1,1)) is proposed in this paper. The new model combines the adjacent sequence operator, therefore the newly generated sequence is less random. By adjusting the model parameters, the structure of the model can be changed, so that the model has the features of selecting the adaptive structure. By comparison, the differential evolution algorithm is selected to optimize the hyperparameters of the model. In particular, the robustness of the model is validated by introducing perturbations to the raw data to imitate errors generated during data collection. Finally, three actual cases of China's hydropower generation, China's natural gas production and China's total primary energy production are predicted; the prediction result shows that the new model has higher prediction accuracy than the other six models. The results indicate that the proposed model benefits from its adaptive structure and produces reliable predictions. According to these prediction results, relevant suggestions on the development of China's energy are provided to decision makers.