The nonhomogeneous grey model has been seen as an effective method for forecasting time series with approximate nonhomogeneous index law, which has been widely used in diverse disciplines on account of its high prediction precision. However, there remains room for improvements. For this, this study presents an improved nonhomogeneous grey model by incorporating the dynamic integral mean value theorem and fractional accumulation simultaneously. In order to promote the efficacy of the optimised model, we apply the whale optimization algorithm (WOA) to ascertain its optimal parameter. In particular, two examples are conducted to validate the superiority of the proposed model in contrast with other benchmarks, and the experimental results show that the mean absolute percentage error of the proposed approach is 808692% and 6.0706%, respectively, indicating the proposed approach performs better than other competing models.

中文翻译：

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改进的分数阶累加非齐次灰色模型及其应用

非齐次灰色模型被认为是一种利用近似非齐次指数规律预测时间序列的有效方法，因其较高的预测精度而被广泛应用于各个学科。然而，仍有改进的余地。为此，本研究通过同时结合动态积分平均值定理和分数累加，提出了一种改进的非齐次灰色模型。为了提高优化模型的有效性，我们应用鲸鱼优化算法（WOA）来确定其最优参数。特别是，通过两个例子来验证所提出的模型与其他基准相比的优越性，实验结果表明所提出的方法的平均绝对百分比误差分别为 808692% 和 6.0706%，