调和平均的组合预测方法之性质研究

调和平均的组合预测是一种非线性组合预测方法．对基于最小几何距离的加权调和平均组合预测模型的性质进行了研究，从理论上说明了该种方法的有效性．首先提出新的非劣性组合预测、优性组合预测、预测方法优超、冗余度的概念；其次指出模型的任一个可行解对应的组合预测至少是非劣性组合预测，并给出优性组合预测存在的一个充分条件；最后证明在一种单项预测方法优超另一种单项预测方法的条件下冗余预测方法出现的判定定理．

Research on properties of harmonic means combination forecasting method

The harmonic means combination forecasting method is a nonlinear one. We study the properties of harmonic means combination forecasting method based on minimizing geometric distance to demonstrate the effectiveness of this method theoretically. First, we propose some new concepts of non_inferior combination forecasting, superior combination forecasting, dominant forecasting method, and redundant degree. Second, we point that the combination forecasting corresponding to the arbitrary feasible solution of this model is at least non_inferior, and we also give the sufficient condition of existence of superior combination forecasting. Finally, we prove the determining theorem of redundant forecasting method under the condition that a single forecasting method dominants another one.