重构相点L_1范数层次组合预测方法

Hierarchical combined forecasting based on L_1 norm of reconstructed phase points

为克服时滞现象对系统状态带来的影响,结合相空间重构理论和组合预测方法,提出一种基于重构相点L1范数的层次组合预测新方法。对于混沌系统状态序列,使用延迟坐标状态空间重构技术进行相空间重构后,应用层次结构组合预测方法研究相点L1范数的演变过程,并通过反解相点L1范数预测值得到原时间序列的预测值。组合预测法中采用AR(p)模型和新陈代谢GM(1,1)模型作为单一预测模型,应用层次结构权值确定方法求取组合预测方法中各模型的组合权重。最后为提高预测精度,使用残差GM(1,1)方法对预测值进行补偿。实验数据的仿真对比分析给出了算法性能评价结果,验证了算法的有效性。

To overcome the damage from the system time delay,a new hierarchical combined forecasting method based on L1 norm of reconstructed phase points is proposed using the phase space reconstruction theory and the combined forecasting method.For chaotic system series,the phase space delay coordinate reconstitution theory is applied to reconstruct the phase space,the hierarchical combined forecasting method is used to analyze the change laws of phase point L1 norm,and forecasting values of time series are obtained with the L1 norm inverse solution.The AR(p)model and metabolism GM(1,1)model are employed as single models while the hierarchical structure based the weight determining method is used to ascertain the weights of each single model.To improve the forecasting precision,residual errors are compensated with GM(1,1)model.The algorithm performance evaluation is obtained by simulating the measured data,and the simulating results verify the method effective.