通过引入三次时间项来构造三次时变参数离散灰色预测模型(简称CDGM(1,1)模型),并对模型的性质进行研究.研究结果表明,CDGM(1,1)模型具有白指数重合性、线性规律重合性、二次规律重合性、三次规律重合性和伸缩变换一致性.运用最优化理论研究了CDGM(1,1)模型的基值迭代问题,并给出了模型的预测步骤和算法.通过算例比较CDGM(1,1)、DGM(1,1)和NDGM(1,1)三个模型的预测效果,结果表明CDGM(1,1)的预测和模拟精度都得到了明显改善.
A cubic time-varying parameters discrete grey forecasting model(referred to as CDGM (1, 1)) is constructed by introducing cubic time-varying terms, whose properties are studied. It is concluded that the CDGM(1, 1) possesses white exponential law coincidence, linear law coincidence, quadratic law coincidence, cubic law coincidence and consistency of stretching transformation. Furthermore, the optimization method is applied to optimize the iterative starting value of the proposed model, and the steps of using CDGM(1, 1) are introduced to predict. Finally, the proposed model is compared with another two discrete grey models through an instance. The results show the proposed model greatly improves the simulation and prediction precision.