Purpose

The purpose of this paper is to summarize progress of grey forecasting modelling, explain mechanism of grey forecasting modelling and classify exist grey forecasting models.

Design/methodology/approach

General modelling process and mechanism of grey forecasting modelling is summarized and classification of grey forecasting models is done according to their differential equation structure. Grey forecasting models with linear structure are divided into continuous single variable grey forecasting models, discrete single variable grey forecasting models, continuous multiple variable grey forecasting models and discrete multiple variable grey forecasting models. The mechanism and traceability of these models are discussed. In addition, grey forecasting models with nonlinear structure, grey forecasting models with grey number sequences and grey forecasting models with multi-input and multi-output variables are further discussed.

Findings

It is clearly to explain differences between grey forecasting models with other forecasting models. Accumulation generation operation is the main difference between grey forecasting models and other models, and it is helpful to mining system developing law with limited data. A great majority of grey forecasting models are linear structure while grey forecasting models with nonlinear structure should be further studied.

Practical implications

Mechanism and classification of grey forecasting models are very helpful to combine with suitable real applications.

Originality/value

The main contributions of this paper are to classify models according to models' structure are linear or nonlinear, to analyse relationships and differences of models in same class and to deconstruct mechanism of grey forecasting models.

中文翻译：

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灰色预测模型总结

目的

本文的目的是总结灰色预测建模的进展，解释灰色预测建模的机理，并对现有的灰色预测模型进行分类。

设计/方法/途径

总结了灰色预测建模的一般建模过程和机理，并根据灰色预测模型的微分方程结构对灰色预测模型进行了分类。具有线性结构的灰色预测模型分为连续单变量灰色预测模型、离散单变量灰色预测模型、连续多变量灰色预测模型和离散多变量灰色预测模型。讨论了这些模型的机制和可追溯性。此外，还进一步讨论了具有非线性结构的灰色预测模型、具有灰色数列的灰色预测模型和具有多输入多输出变量的灰色预测模型。

发现

清楚地解释了灰色预测模型与其他预测模型之间的差异。累积生成运算是灰色预测模型与其他模型的主要区别，有助于在有限数据下挖掘系统发展规律。绝大多数灰色预测模型是线性结构的，而具有非线性结构的灰色预测模型有待进一步研究。

实际影响

灰色预测模型的机理和分类对于结合合适的实际应用非常有帮助。

原创性/价值

本文的主要贡献是根据模型的结构是线性的还是非线性的对模型进行分类，分析同类模型之间的关系和差异，解构灰色预测模型的机理。