Predicting China’s elderly population by using a fractional grey prediction model with time power term

Accurate prediction of the aging population can provide valuable reference and corresponding theoretical support for the adjustment of national population development policy and economic development strategy. To explore the future development trend of China’s aging population, this paper establishes a novel fractional grey prediction model with the time power term (abbreviated as FGM (1, 1, t α ) model) to study China’s aging population. FGM (1, 1, t α ) has the properties of fractional order accumulation operation and GM (1, 1, t α ) model, which makes it good at capturing nonlinear features in time series. Furthermore, the quantum genetic algorithm is used to search for unknown parameters in the model to facilitate the solving task of the model. Data on China’s aging population from 2000 to 2009 are used to train the prediction models, and data from 2010 to 2019 are used to evaluate the models’ prediction performance. The results show that the FGM (1, 1, t α ) model outperforms the other competing models, which means that it has good generalization. Finally, the FGM (1, 1, t α ) model is used to forecast China’s aging population from 2020 to 2029.