In this study, in order to reduce the morbidity and improve the structural stability of the existing grey multivariable convolution forecasting model, a new derived multivariable grey model based on the derivation method, abbreviated as DMGM (1, n), is presented. Firstly, the time response formula of DMGM (1, n) is deduced by derivation method, which can avoid solving the inverse matrix so as to reduce the morbidity of the model. Secondly, the parameter identification of the model is given based on the least-squares method. Then, it is proved theoretically that DMGM (1, n) is superior to GMC (1, n) because the solution of the former overcomes the shortcoming of the latter that the original model does not take full advantage of all the information from the raw data for modeling. Finally, three real cases with different variables were performed. The fitting and prediction results indicate that DMGM (1, n) is better than GMC (1, n) and the other multivariate grey prediction models in these cases, which also demonstrates that this novel model outperforms the other grey models in this paper.

为了减少现有灰色多变量卷积预测模型的发病率并提高其结构稳定性，本文提出了一种基于推导方法的新的多变量灰色模型，简称为DMGM（1，n）。首先，通过推导方法推导了DMGM（1，n）的时间响应公式，可以避免求解逆矩阵，从而降低了模型的发病率。其次，基于最小二乘法对模型进行参数辨识。然后，从理论上证明DMGM（1，n）优于GMC（1，n），因为前者的解决方案克服了后者的缺点，即原始模型没有充分利用原始数据中的所有信息进行建模。最后，进行了三个具有不同变量的实际案例。拟合和预测结果表明，在这种情况下，DMGM（1，n）优于GMC（1，n）和其他多元灰色预测模型，这也表明该新颖模型优于本文中的其他灰色模型。