线性时变参数离散灰色预测模型

Linear time-varying parameters discrete grey forecasting model

分析离散灰色模型模拟值增长率恒定的原因,通过引入线性时间项,构造时变参数离散灰色模型(称TDGM(1,1)模型).进而研究该模型性质,结果表明:TDGM(1,1)模型具有白指数规律重合性、线性规律重合性、伸缩变换一致性,克服了原离散模型模拟值为等比序列的问题.应用最优化方法研究TDGM(1,1)模型迭代基值问题,建立优化模型并提出求解算法.最后说明应用TDGM(1,1)模型进行建模和预测的步骤,通过实例比较该模型与原离散灰色模型及非其次离散模型的预测能力,结果显示TDGM(1,1)具有更高的模拟和预测精度.

This paper analyzed the reason for invariable growth rates of the DGM（1,1） model＇s simulated values. In order to overcome that shortcoming, a new time-varying parameters discrete grey model （which is called TDGM（1,1）） was constructed by introducing linear time-varying terms. Then, this paper researched properties of the new model, and reached the conclusion that TDGM（1,1） not only possessed white exponential law coincidence, linear law coincidence and consistency of stretching transformation, but also solved the problem that simulated values of original DGM（1,1） were geometric sequences. Furthermore, the paper applied optimization method to optimizing the iterative starting value of the new model, and introduced the steps of using TDGM（1,1） to predict. Finally, the new model was compared with another two discrete grey models through an instance. The results prove the new model greatly improves the simulation and prediction precision.