Evaluating the effect of sample length on forecasting validity of FGM(1,1)

Three indicators (GDP, PCDIIP-rh and Total Population) are selected in this paper to study the effect of sample length on forecasting validity of FGM(1,1). It has passed the test, such as development coefficient, mean relative error within the sample, and ratio of mean square error. The above three sets of indicators are proved to be suitable for FGM(1,1) to make predictions. The results of the study indicate that the forecasting of 4–6 sample lengths is the most appropriate. The MAPE of 5 sample length is better than sample lengths 4 or 6. The conclusion of this study is verified by taking the oil production of India and Canada as examples. On this basis, the sample length 5 is selected to predict the average annual concentration of PM2.5 from 2019 to 2021 in Xingtai. The forecasting results show that the PM2.5 in Xingtai will decline in the next three years, but it will not reach the national level 2 concentration limit.