GM(1,1)模型背景值的优化

背景值是影响GM(1,1)模型精度的关键因素之一。当前背景值优化的改进模型均取得较好的效果,但优化后的背景值公式多数比较繁琐,并且部分优化模型不适用于高增长型序列。本文根据模型的指数性质以及积分特点,分析背景值的构造原理,利用黎曼积分的核心思想,提出以不规则梯形面积取代传统梯形面积构造法,对传统GM(1,1)模型背景值进行优化。通过实验验证了新模型具有白指数律重合性,不仅适用于低增长指数序列,亦适用于高增长指数序列,并且优化公式简单,具有较高的实用性与可靠性。

Dynamic Pricing with Consumers' Double-entry Mental Accounting and Reference Effects

The background value is one of the key factors influencing the accuracy of GM(1,1) model.The improved models by optimizating background value are effective at present.But a lot of the optimized formulas are complicated and part of them are also not suitable for the high growth series.According to the exponential properties and intergral characteristics of model, the structure principle of background value is analyzed, and a new construction method is proposed in this paper using the irregular trapezoid to replace the traditional one based on the core idea of Riemann integral,so as to achieve optimizing model.The test results showed that the optimized model possessed white exponential law coincidence property,it could be applied to low-rising exponential series,and also could be the same with high-rising one.Thus,the test verified the improved GM(1,1) model with simpler formula was higher in practicality and reliability.