灰色预测法的进一步推广及应用

把原始时间序列进行多次累加,产生多个新序列,研究它们之间的关系,建立多元线性(或非线性)回归模型.给定显著性水平α,对回归方程进行显著性检验,在置信度1-α下,利用微分,差分关系建立相应的高阶微分方程,从而实现对原序列的预测或控制.该方法进一步推广了灰色预测法,为时间序列建模提供了一个新手段,一些著名的微分方程模型成为这一方法的特例,最后,用该方法对中国1979年至2008年的GDP序列建立微分方程模型并进行预测.

Further Promition and Application Based on Gray Prediction Method

The original time series is accumulated several times to produce some new sequences,research the relationships between them,establish the multiple linear,or nonlinear regression model.Given the level of significance α,carry out the significance test for the regression equation,establish the corresponding higher order differential equations in confidence level 1-α,via relations with differential and difference.In order to achieve forecasting or control for the original series.The method further promote the gray prediction,provides a new way for time series modeling.Some well-known differential equation models become as a special case of this approach modeling.Finally,use the method to establish differential equations for the GDP of China from 1979 to 2008,and to predict the GDP in 2007,2008.