具有L_(2)正则项的新型离散多变量灰色预测模型

A Novel Discrete Multivariate Grey Forecasting Model with L_(2) Regularization Term

MGM(1,m,N)模型存在参数非同源、模型结构简单、变量间易产生多重共线性三个问题.为解决模型不足,在MGM(1,m,N)模型中引入线性修正项和灰色作用量,以完善模型结构;利用导数一阶差分公式和递归法求解模型的时间响应式,以解决MGM(1,m,N)模型参数非同源性问题;为解决模型变量间多重共线性带来的不良影响,从减小参数估计量的方差角度出发,将L_(2)正则项引入普通最小二乘估计中,并通过粒子群算法求解最优L_(2)正则化参数.最后,将新型多变量灰色预测模型应用到中国三大主粮产量预测中.结果表明:新型多变量灰色预测模型从一定程度上解决了MGM(1,m,N)模型在参数应用和模型结构方面存在的问题,有效解决了多重共线性对模型预测性能的影响,有效提高了MGM(1,m,N)模型的预测精度.

The MGM(1,m,N) model has three problems:Non-homologous parameters,simple model structure,and multicollinearity between variables.In order to solve this defects of MGM(1,m,N) model,the new structure MGM(1,m,N) is built,which modifies the model structure by introducing the linear correction term and the grey action term into the original model.In order to solve the defects in the parameter application,using the derivative first-order difference formula and recursive method to solve the time response function of NSMGM(1,m,N) model.To address the adverse effects of multicollinearity,the parameter estimation method is improved from reducing the variance of parameter estimators.The L_(2) regularization term is introduced into the ordinary least square estimation and the optimal L_(2) regular term parameter is solved by the particle swarm algorithm.Finally,the novel model is applied to the forecast of China's three major staple grain yields.The results show that the novel model solves the problems in the parameter application and model structure of MGM(1,m,N) model in certain degree.The optimized model can effectively alleviate the influence of model's predictive performance by multicollinearity and improves the MGM(1,m,N) the model's predictive precision.