中文摘要：

In order to deeply research the structure discrepancy and modeling mechanism among different grey prediction models, the equivalence and unbiasedness of grey prediction models are analyzed and verified. The results show that all the grey prediction models that are strictly derived from x(0)(k) +az(1)(k) = b have the identical model structure and simulation precision. Moreover, the unbiased simulation for the homogeneous exponential sequence can be accomplished. However, the models derived from dx(1)/dt + ax(1)= b are only close to those derived from x(0)(k) + az(1)(k) = b provided that |a| has to satisfy|a| < 0.1; neither could the unbiased simulation for the homogeneous exponential sequence be achieved. The above conclusions are proved and verified through some theorems and examples.

英文摘要：

In order to deeply research the structure discrepancy and modeling mechanism among different grey prediction models, the equivalence and unbiasedness of grey prediction models are analyzed and verified. The results show that all the grey prediction models that are strictly derived from x^（0）（k） ＋az^（1）（k） = b have the identical model structure and simulation precision. Moreover, the unbiased simulation for the homogeneous exponential sequence can be accomplished. However, the models derived from dx^（1）/dt ＋ ax^（1）= b are only close to those derived from x^（0）（k） ＋ az^（1）（k） = b provided that ｜a｜ has to satisfy｜a｜ 0.1; neither could the unbiased simulation for the homogeneous exponential sequence be achieved. The above conclusions are proved and verified through some theorems and examples.