振荡型GM(1,1)幂模型及其应用

针对现实世界广泛存在的小样本振荡序列建模和预测问题,提出含有系统延迟和时变参数的振荡型GM(1,1)幂模型。给出最小二乘准则下的两级参数包计算公式,在此基础上构建非线性优化模型以寻求最佳幂指数和时间作用参数,以此识别原始数据所蕴含的振荡特征。将该模型应用于应急资源需求预测,并将建模结果与传统GM(1,1)幂模型、ARIMA和EMD-ARIMA方法进行比较,结果表明振荡型GM(1,1)幂模型具有较高的精度。

Oscillating GM(1,1) power model and its application

In view of the problem of modeling and forecasting for small sample oscillating series, which exists widely in the real world but to be paid less attention by people, this paper proposed oscillating GM(1,1) power model with system latency and time-varying parameters. The two ranks’parameters package formula is presented under the least squares criterion. On this basis, a nonlinear optimization model is employed to seek the best exponent and time interaction parameters, in order to identify the oscillating characteristics behind raw data. Finally, the proposed model is applied to forecast emergency resource demand, and the modeling precisions are compared among the traditional GM(1,1) power model, ARIMA and EMD- ARIMA. The results show that the oscillating GM(1,1) power model has the highest accuracy.