封闭人群生存人数整体预测--以Lee-Carter模型为例

由不同组别人群组成封闭人群整体生存人数的预测是相关经济、社会问题研究的基础。现有文献在研究相关问题时，使用的方法为：首先根据动态死亡率模型对其中具有相同特征不同部分的生存人数进行预测，之后通过加总得到整体人数的预测（简称现有方法）。由于现有方法忽略了不同特征人群死亡率变动间相关性的影响，会低估生存人数的波动性。本文使用Lee?Carter模型，在将封闭人群按性别分组的基础上，给出了构建生存人数整体预测模型的过程和实例。并通过理论分析和数值模拟两个视角对现有方法和新方法做了比较。比较结果指出：在死亡率波动具有广泛相关性的现实世界中，只有在均值预测时，现有方法才可以达到预期效果，因此笔者建议在对整体人数（特别是涉及方差和分布函数）预测时，使用本文介绍的整体生存人数预测模型。

Forecasting the Whole Number of the Survival in Isolated Population：Using Lee-Carter Model

Forecasting the survival’ s number of isolated population consisting of various groups, is the base of the related economic, social issues research. However, when studying the related problems, a general way of obtaining prediction is to estimate expectation of each group’ s survival’ s number, which is categorized according to some characteristics, and then the whole survivors ’ s number can be obtained by summing them. Since this method ignores the correlation of between the different characteristics of the population, the volatility of survival’ s number of people is usually underestimated. In this paper, the Lee?Carter model will be extended by capturing mortality correlations between groups, and we can obtain the whole survival’ s number in one step, using the extended model. Then the existing methods and new methods are compared by theoretical analysis and numerical simulation methods. The conclusion is, only when the expectation can be accurately estimated by the two methods, the old methods can’ t work well both in predicting variability and distribution, so the new method is recommended.