灰色区间预测模型及其性质

Grey interval forecasting model and its properties

针对振荡幅度大的小样本振荡序列预测问题,构建灰色区间预测模型.首先对原始序列的上下界序列直接建立非等间隔GM(1,1)模型,得到取值包络带的上下包络曲线以描述系统发展的边界;然后给出原始序列区间预测值和基本预测值的计算方法,建立区间预测算法;最后研究区间预测模型的灰指数规律性和时效性.数值实验揭示,发展系数的取值不是影响区间预测模型时效性的唯一因素;应用实例表明,所提出方法能够有效地提高序列的预测精度.

In order to forecast the small sample large oscillating sequences, this paper proposes a grey interval forecasting method. Firstly, two non-equidistance GM（1,1） models are built for upper and lower sequences respectively, and the development boundary of the system are described by the upper and lower envelope curves. Then, the computing method for the interval and basic forecasting values of the original sequence are proposed, and the algorithm is constructed. Finally,the grey exponent law and timeliness of interval forecasting model are studied. The numerical experiment shows that the value of the development coefficient is not the only factor influencing the timeliness. The application example shows that the forecasting accuracy can be effectively enhanced.