Gray fuzzy prediction model is suitable for small-sample-size prediction. The real per capita disposable income of urban residents in Hebei Province used as an example, and samples 3–35 in length selected, the influence of sample length on prediction performance of the GM (1,1) model were investigated. Sample length presents a nonlinear relationship with the predicted relative error of the model. Compared with large samples with lengths more than 15, small samples with lengths below 15 are suitable to establish the gray fuzzy prediction model. Small samples with length of 8–13 are applicable to three-step prediction. Sample lengths suitable for modeling were proposed, and the above conclusions provide a certain theoretical foundation and guidance for the research and application of gray fuzzy prediction in the future.

中文翻译：

---

样本长度对灰色模糊预测性能的影响

灰色模糊预测模型适用于小样本量的预测。以河北省城镇居民实际人均可支配收入为例，选取3〜35个样本，研究了样本长度对GM（1,1）模型预测性能的影响。样本长度与模型的预测相对误差呈非线性关系。与长度大于15的大样本相比，长度小于15的小样本适合建立灰色模糊预测模型。长度为8–13的小样本适用于三步预测。提出了适合建模的样本长度，以上结论为今后灰色模糊预测的研究和应用提供了一定的理论基础和指导。