本文针对波动性上升或下降的时间序列，提出了一类基于广义等高线的灰色波形预测模型。该模型通过拟合带时间趋势项的最小二乘估计确定等高线斜率，并基于此斜率在原始数据序列最小值和最大值之间选取一系列平行直线作为广义等高线，进而对等高时刻序列各元素横坐标进行GM（1，1）建模和预测。通过对我国民航客运量及近期原油价格的预测对模型进行检验，本文得出基于广义等高线的灰色波形预测模型能够实现对波动性上升和下降的时间序列的预测，并提高了灰色波形预测模型预测此类数据的准确性。此外，由于灰色波形预测模型所需样本量较小，本文提出的模型有助于对新兴事物发展变化的预测。
In this paper, a modified grey wave forecasting model with generalized contour lines is proposed to forecast time series which is increasing (or decreasing) and fluctuating with time. The modified model identifies the slope of contour lines through a linear regression model with time trend and estimates the regression model with ordinary least square method. And then a set of parallel lines between the minimum and maximum values of original data series are chosen as the generalized contour lines. In the last step, GM(1,1) models are established based on the elements in generalized contour time sequences. In the empirical analysis, the proposed model is used to forecast Chinese airline passenger volume, which fluctuates with increasing trend and crude oil price, which fluctuates with decreasing trend in the past several months. The result indicates that grey wave forecasting model with generalized contour lines can improve the accuracy of grey wave forecasting model with horizontal contour lines. Also it is useful to forecast the development of emerging things, since it just uses relatively few sample data.
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