灰色预测和时序预测的探讨

本文讨论了灰色模型,特别是GM(1,1)模型的特点和适用范围,并将GM(1,1)模型和时序AR(n)模型结合起来(称为组合模型),对我国轻工业产量发展指数等三个项目分别进行了组合模型预测。结果表明,在一般GM模型中引入AR模型可显著提高预测的准确度;在非平稳时序建模中引入GM模型,可作为提取趋势项的另一种方法。文中还从预测的角度将灰色模型和时序模型进行了比较和分析,对“灰”的物理概念进行了初步探讨。

On Forecasts by Grey Model and Time Series Model

The specific features and the scope of application of Grey Model(GM), especially GM(1,1), are discussed. GM(1,1)is combined with time series AR model for forecasting purposes. The combined model has been used in the prediction of three projects including the production growth rate of China's light industry. The results sho wthat the accuracy by the combined model is better than that by GM(1,1), It is suggested that GM(1,1) modle be used for cases with an exponential trend in a non-stationary time series instead of the regressive method so far used, and that GM (2,1)be used in the case of a harmonic trend.A comparison between Grey Model and time series model for forecast shows that:1. GM(1,1)is good for exponential case and ARMA model for cases with stationary data; one can be explained by the other.2. GM(1,1) is an expression for an inertial system and that is why GM(1,1) has been found successful in social and economic prediction.3. "Grey" here means that system factors, model structure and order are known while model parameters have to be estimated.4. The systems represented by either ARMA or difference model are even "greyer" than those represented by GM because the order of the former is yet to be found in modelling and the order of the latter is already known.