多变量时滞阻尼累加灰色模型及其应用

Multivariable time-lag damping accumulated grey model and itsapplication

基于现实行为系统中存在的时滞效应和多变量灰色预测系统中需区分新旧信息及预测趋势不可控的情况,通过引入改进的阻尼累加生成算子与时滞系数,提出多变量时滞阻尼累加灰色模型(TLDAGM(1,N))及其扩展形式,模型理论上可达到与传统多变量灰色预测模型的兼容性;讨论模型的参数估计方式及求解方法,给出模型的参数优化方法及具体的建模步骤;将该模型应用于我国高新技术企业产值及河南省粮食产量预测问题中,并与传统多变量灰色预测模型进行比较.结果表明:所提模型的模拟精度和预测精度均显著优于传统多变量灰色预测模型,新模型能够较好地识别多变量行为系统数据中包含的时滞性、重要性及时间序列的趋势因素.实例分析的结果验证了所提模型的合理性、适用性和有效性.

Based on the time-lag effect in the realistic behavior system and the need to distinguish the old from the new information and the uncontrollable prediction trend in the multivariable grey prediction system,by introducing an improved damping accumulated generation operator and time-lag coefficient,a multivariable time-lag damping accumulated grey model(TLDAGM(1,N))and its extended form are proposed,which can theoretically achieve compatibility with traditional multivariable grey prediction models.The parameter estimation method and solution method of the model are discussed,the parameter optimization method and specific model steps of the model are given.Finally,the model is applied to the prediction of the output value of high-tech enterprises in China and the grain yield in Henan province and compared with the traditional multivariate grey prediction model.The results show that the simulation accuracy and prediction accuracy of the proposed model are significantly better than those of the traditional multivariable grey prediction model.The model is able to better identify the time-lag,validity,significance and trend factors of the time-series contained in the data generated by different factors in the multivariable system at different times.The results of the empirical analysis verify the rationality,applicability and validity of the proposed model.