摘要
针对灰色预测模型的适应范围和优化问题,首先根据灰色GM(1,1)模型参数是灰的、可调的原理,提出了GM(1,1,β)模型的内涵型和参数包形式,分析了模型的若干性质,然后给出了模型的优化算法.研究结果表明,GM(1,1,β)灰微分方程模型参数a的客观取值范围为(-∞,+∞),经典GM(1,1)模型参数a的客观取值范围为(-2,+2);发展系数a的客观取值范围是由背景值系数β决定的,而与原始数据无关;灰微分方程模型完全适合齐次指数数列.最后,以我国城镇居民家庭人均可支配收入的数据为例验证了GM(1,1,β)灰微分方程模型的有效性.
As to the applied range and optimization of grey forecast model, according to the principle that grey GM(1,1) model's parameters are grey and adjustable, the connotation model and parameter packet formulas of CM(1,1,β) were put forward in this paper, and some properties of the model and model's optimization algorithm was analyzed. The results show that the objective valuing region of parameter a of GM(1,1,β) model is (-∞, +∞), and the objective valuing region of parameter a of GM(1,1) model is (-2, +2), the objective valuing region of parameter a is determined by the background value coefficient, and it has nothing with raw data sequence; GM(1,1,β) grey differential equation completely suits for the homogeneous exponential function series. Finally, the example of simulating and forecasting the per capita income of urban dwellers in China shows that the grey differential equation GM(1,1,β) is valid.
出处
《系统工程理论与实践》
EI
CSSCI
CSCD
北大核心
2014年第5期1249-1255,共7页
Systems Engineering-Theory & Practice
基金
国家科技计划项目(2011BAD21B0601)
国家自然科学基金(41271235)