基于灰色组合模型的河南省粮食产量预测

一元线性回归有直线趋势,而GM(1,1)能较好地模拟指数变化的趋势。但是,如果原始序列整体上是直线趋势,在少数点上,数据模拟值和回归直线偏离较大时,线性函数已不能很好地预测数据序列的变化了。对于此类问题,将数据分为跳变点(即模拟值偏离回归直线较大)和非跳变点数据,并将跳变点又分为上、下跳变点,借鉴灰色灾变预测原理,用GM(1,1)模型预测跳变点数据,而对其他非跳变点使用去掉跳变点后的数据形成的新的线性回归方程进行预测。通过对河南省粮食产量的预测,结果表明该方法很好地克服了GM(1,1)模型和线性回归模型的缺陷,具有较好的实际应用价值。

Prediction of Grain Production In Henan Province by Grey Combined Model

One-variable linear regression analysis could reflect the tendency of straight line while GM(1,1)could do it better when the sequence tends to change as exponential function.However,if a raw sequence has straight tendency in a whole but there exists big error between actual and fitted values among some points,line function will no more predict accurately the changing tendency of the data sequence.To solve this question,firstly,the raw data sequence with some abnormal data is classified into two parts:aberrant data and normal data,more over,we could classified the aberrant points into upper and lower aberrant points;secondly,borrowing the principle of grey disaster,we can make use of GM(1,1)to forecast the possible aberrant date points in the future based on the aberrant data,and for other normal data points left,one new linear regression function can be applied to get a forecasted value.By appling the combined method to the prediction of the grain production of He'nan province,we find the new method could achieve better forecasting results compared with other forecasting models,and make up for some deficiencies in GM(1,1)model and linear regression in a sense.