为了解决固定模型预测时变系统容易出现较大误差的问题,提出模 型更新算法,即采用将移动窗算法与传统灰色预测模型相结合的方法.通过在建模 序列中删除一部分旧数据、纳入一部分新数据的方式递推更新预测模型,并分解数 学模型所涉及的关键量~$a\mathrm{\&}b$ 从而简化递推数学公式;利用国家统计年鉴的统计数据验证上述方法的有效性.为了解 决传统灰色预测模型建模长度选择的问题,而递推算法能在已知模型参数基础上通 过简单计算获得新模型的各项参数,文章给出了详细的递推数学公式;另外对于最小 建模长度~$L_{min}$ 也进行讨论,认为~$L_{min}\ge 3$,并给出证明.所改进算法提高灰色模型的预测精度,同时也为最优序 列长度计算提供理论依据.

For solving the problem that being easy to have big error through fixed model monitoring time varying system, the methods combing moving windows algorithm with grey prediction algorithm (MWGM(1,1)) was proposed, describing detailed recursive algorithm to update prediction model adopting the way of removing part of past data from modeling sequence and absorbing new ones from sampling data, and key quantities of prediction math model that were $a\mathrm{\&}b$ were decomposed in order to simplify recursion formula, then describing how to determine the length of windows were, and finally the effectiveness of such MWGM(1,1) algorithm was tested by actual statistics data. for solving the problem to select the optimal sequence length of grey model, the recursive algorithm which could get parameters of new model from parameters of known model was proposed and this paper described recursion mathematical formula in detailed. Furthermore, the problem to solve the minimum length of modeling was described too, and the result that $L_{min}\ge 3$ was proved. After all the improved algorithm could improve prediction accuracy and supply theory for optimal sequence length.