分数阶累加时滞GM(1,N,τ)模型及其应用

基于系统的时滞性,本文建立了时滞灰色GM(1,N,τ)模型,给出了模型的最小二乘参数估计公式以及模型的解析解.在引入分数阶累加生成算子后,将原模型扩展为分数阶累加GM(1,N,τ)模型,当时滞值为非整数情况时,采用相邻整数点加权构造法,完善了模型;通过粒子群算法确定模型最优的分数阶累加生成阶数.最后本文结合武汉市1995-2008年14年科技投入及经济增长的实际背景,分别建立了经典时滞GM(1,N,7)和分数阶累加时滞GM(1,N,7)模型对GDP数据做了预测,比较了两个模型预测结果,发现分数阶累加时滞GM(1,N,7)模型具有更高的建模精度.

Fractional order accumulation time-lag GM(1,N,τ) model and its application

Based on the time lag effect of system, this paper constructs the time-lag GM(1,N,τ) model, and provides its least squares parameter estimation formula and analytical solution. Then introducing fractional order accumulation generation operator, GM(1,N,τ) is transformed into fractional order accumulation time-lag GM(1,N,τ), offering adjacent integer points weighted method when time-lag value is not integer, determining the time-lag value via particle swarm optimization. Finally, we test the original GM(1,N,τ) and fractional order accumulation time-lag GM(1,N,τ) by using the real data of R&D investment and GDP in Wuhan from 1995 to 2008. The example indicates that the accuracy of fractional order accumulation time-lag GM(1,N,τ) is more satisfactory.