参数和背景值同时优化的GM(1,1)模型

Optimized Parameter with Integrated Background Value for GM(1,1) Model

为了改进原始GM(1,1)模型的模拟效果,优化GM(1,1)模型的背景值后,利用最小二乘法,得到发展系数a.在a已知的条件下,根据GM(1,1)模型的还原值与实际值之差最小,求出待定系数c,从而获得参数和背景值同时优化的GM(1,1)模型.此模型不需要选择初始条件,具有白化指数律重合性.实例表明此优化模型既能模拟低增长序列,又能模拟高增长序列,具有较好的模拟效果和预测效果.

In order to improve the simulative results of the original GM（1,1） model, after the background value of GM（1,1） model is optimized, by the method of the least squares, the development coefficient -a is obtained. Under the condition that a is known, the undetermined coefficient c is obtained when the difference of the recuperating values and the real values of GM（1,1） model is the smallest, and the optimized parameter with integrated background value for GM（1,1） model is obtained. This model does not need to select the initial condition, and has the white exponential law of coincidence. The examples are used to indicate this optimized model can simulate both the low-growth series and the high-growth series, furthermore has the better simulative results and the better predictive results.