时变参数GM(1, 1) 幂模型及其应用

为了进一步增强灰色预测模型对原始数据的适应能力,提出一种时变参数GM(1,1)幂模型,通过引入多项式函数描述GM(1,1)幂模型的结构参数随时间的动态变化规律。根据建模样本量的不同,分3种情形给出了模型的参数辨识算式,同时给出了时变参数GM(1,1)幂模型白化方程的解析解,利用积分复合梯形公式将其转化为可用于预测的离散时间响应式,并提出了参数优化方法。应用实例表明,时变参数GM(1,1)幂模型比固定参数GM(1,1)幂模型具有更高的模拟和预测精度。

GM(1, 1) power model with time-varying parameters and its application

In order to further enhance the adaptive capacity of the grey forecasting model to original data, a GM(1, 1) power model with time-varying structure parameters is proposed. Polynomial functions are introduced to describe the dynamic changes of the structure parameters with time. According to the different modeling sample sizes, the identification formulas for unknown parameters are given under three kinds of situations. At the same time, the analytical solution to white differential equation of GM(1, 1) power model with time-varying parameters is proposed. The integral compound trapezoid formula is employed to transform the continuous solution into discrete time response that can be used to predict. An application example shows that the GM(1, 1) power model with time varying parameters has higher simulation and forecast precision than that of the GM(1, 1) power model with fixed parameters.