含负值序列的GM(1,1)模型的一种优化方法

An Optimization Method for Constructing GM(1,1) Model with Series Containing Negative Numbers

经典GM(1,1)模型要求处理的序列为非负,但实际应用中含负值序列比较常见,有必要建立适合含负值序列的GM(1,1)模型.现有的处理方法是将原含负值序列X沿纵轴平移一个固定常数c使原序列变为非负,然后按经典GM(1,1)建立模型,再对所得的模拟序列进行逆变换,从而得到原含负值序列的摸拟值和预测值.由于现有方法中所取c值是固定的,其模型精度不一定达到最高.本文提出在区间寻找一个最佳的平移值c,使得现有方法中所取平移值为本文取值范围的一个特例,从而推广了现有方法的结果且模型精度有所提高.模拟结果表明,在区间中选取最佳平移值比固定平移选取的c值提高了模型精度.

Theclassical GM（1, 1） model requires nonnegative raw series, but many practical series may contain negative numbers, so it is necessary to establish GM （1,1） models suitable for those series containing negative numbers. The existing processing method is to translate the series to a nonnegative one by moving up a distance c along the vertical axis, then establish theclassical 6M （1, 1） with the translated nonnegative series. Since the distance c is fixed in the existingmethods, the model precision may not be the highest. This paper presents a method to search an optimal translation valuec in interval, which contains the existing methods as special cases. The simulation results showthat theoptimal translation valuec in this paper improves themodel＇s precision.