Huizhou resident population, Guangdong resident population and elderly population forecast based on the NAR neural network Markov model

We propose a nonlinear auto regressive neural network Markov model (NARMKM) to predict the annual Huizhou resident population, Guangdong resident population and elderly population in China, and improve the accuracy of population forecasting. The new model is built upon the traditional neural network model and utilized matrix perturbation theory to study the natural and response characteristics of a system when the structural parameters change slightly. The delay order and hidden layer number of neurons has a greater effect the prediction result of NAR neural network model. Therefore, we make full use of prior information to constrain and test when making predictions. We choose reasonable parameter settings to obtain more reliable prediction results. Three experiments are conducted to validate the high prediction accuracy of the NARMKM model, with mean absolute percentage error (MAPE), root mean square error (RMSE), STD and R². These results demonstrate the superior fitting performance of the NARMKM model when compared to other six competitive models, including GM (1, 1), ARIMA, Multiple regression, FGM (1, 1), FANGBM and NAR. Our study provides a scientific basis and technical references for further research in the finance as well as population fields.