The effect of sample size on the grey system model

Some forecasting models have been developed, each has its own application condition. The grey model is used for small sample forecasting, but until now there is no reasonable explanation for the reason why it is not used for large sample. Therefore, in this paper, matrix perturbation theory is employed to explain the reason. The results of practical numerical examples from previous works demonstrate that the small sample usually has more accuracy than the large sample when establishing grey model in theory. Furthermore, we used the grey model with small samples to analyse the trend of syphilis incidence in China.