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Based on particle swarm optimization (PSO), a new exponential time delay fraction order grey prediction model is proposed in this paper. Firstly, the original data is preprocessed by fractional-order accumulation; on the basis of fractional-order accumulation, it is proved that the initial value of the original sequence satisfies the fixed point theorem. On the basis of GM(1,1) model, a new model is established by adding exponential time delay term. The model is discretized by integral, the least square estimation of the linear parameters and the approximate time response equation are obtained. Finally, PSO is used to search the optimal parameters of the model and the experimental results are verified by Wilcoxon rank sum test. In order to test the good adaptability and strong prediction ability of the new model, two groups of data are verified for the production and consumption of oil and electricity in China. The results show that the new model has better prediction accuracy and adaptability than the other existing six grey models.

A Novel Exponential Time Delayed Fractional Grey Model and Its Application in Forecasting Oil Production and Consumption of China