应用多项式系数统计模型的人口预测

Population Prediction Based on Polynomial Coefficient Statistical Model

首先将全国1985—2010年人口数据分成两部分,对1985—2010年人口数据进行处理;然后以人口年增长量为样本建立多项式系数模型,根据BIC准则,利用最小二乘法和岭回归方法对模型进行参数估计;最后根据回归方程对2009—2010年人口数据进行预测。根据1985—2008年人口数据得到当阶数p=7,次数r=1,延迟d=6时人口预测效果最佳,拟合精度为8.308 5e-5。同时模型对2007—2010年人口的预测误差率分别为0.000 8%、0.013 4%、0.033 0%、0.064 1%。研究结果显示:该方法在人口预测方面优于BP神经网络、GM(1,1)等方法。

We divided the data of population during 1985 to 2010 into two parts. We built polynomial coefficient auto regressive （PCAR） model based on annual increment. And we predicted the popula- tion of 2009--2010 with the estimated regression model, according to BIC. We used least squares method and ridge regression to get the optimal model when p = 7, r = 1 and d = 6, according to the da- ta of 1985--2008. The fitting accuracy was 8. 308 5e-5. The error rates of the PCAR model of 2007--2010 were 0. 000 8%, 0. 013 4% ,0. 033 0%, and 0. 064 1%. The result of prediction ex- plained that the polynomial coefficient autoregressive model was better than BP neural network, GM （ 1,1 ） model.