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基于机器学习的Lee-Carter模型死亡率预测方法研究
作者: 陶祥兴,杨峥,季延颋
单位: 浙江科技学院 理学院, 浙江 杭州 310023
关键词: Lee-Carter 模型; ARIMA 方法; ARIMA-LSTM 方法; 分数 O-U 过程; 死亡 率预测
分类号:C921
出版年,卷(期):页码:2022(06):47-57
摘要:
世界各国人口死亡率不断降低, 预期寿命变得难以预测。改进死亡率预测方法, 准确预测未来人口的数量变化有着重要意义。传统的 Lee-Carter 模型通过年龄组平均死亡率、时间项以及年龄因子随时间变化的敏感度这三个参数来刻画死亡率的变化, 模型中的时间项采用 ARIMA 方法进行预测。但该方法并不能解决死亡率数据具有长记忆性的问题, 并且现有研究很少将传统人口学方法与大数据背景下机器学习方法相结合。因此本文引入 LSTM (长短期记忆深度学习神经网络) 和分数布朗运动驱动的 O-U 过程来对死亡率预测进行改进。由于中国大陆有关死亡率的数据样本量少且不完整, 选用中国香港男性分年龄组死亡率数据, 分别采用时间序列 ARIMA 方法、时间序列与机器学习相结合的ARIMA-LSTM 方法以及分数 O-U过程来拟合和预测模型中的时间项, 通过残差图和三种评价指标值来比较三种方法的短期预测效果。结果表明, ARIMA-LSTM 方法的短期预测效果最好, 证明了引入机器学习方法对死亡率预测方法改进的可行性, 为政府预测未来死亡率提供新思路, 也为相关机构研究长寿风险提供依据。

The death rate of the world’s population has been continuously reduced, and the
life expectancy has become unpredictable. Therefore, it is of great significance to improve
the mortality prediction method to accurately predict the future population changes. The traditional Lee-Carter model describes the change of mortality through three parameters: the average mortality rate of the age group, the time term and the sensitivity of the age factor to
change with time. The time term in the model is predicted by ARIMA method. However, the method can not solve the problem of long memory of mortality data, and the existing research rarely combines traditional demographic methods with machine learning methods in the context of today’ s big data. Therefore, this paper introduces LSTM ( long-term and short-term memory deep learning neural network) and fractional Brownian motion driven O-U
process to improve the prediction of mortality. Due to the small sample size and incomplete data on mortality mainland China, this paper selects the mortality data of male age groups in Hong Kong, China, and used time series ARIMA method, the ARIMA-LSTM method combined with time series and machine learning, and the fractional O-U process to fit and predict the time items in the model, and compares the short-term prediction effects of the three methods through residual diagram and three evaluation index values. The results show
that ARIMA-LSTM method has the best short-term prediction effect, which proves the feasibility of introducing machine learning method to improve the mortality prediction method, provides a new idea for the government to predict future mortality, and also provides a certain basis for relevant institutions to study the risk of longevity.
基金项目:
国家自然科学基金面上项目 “若干非标准核奇异积分及相关分数次非线性方程的研究”(11771399); 2020 年度浙江省哲学社会科学重点研究基地课题 “基于随机时滞模型的长寿风险量化理论与催化从策略研究”(20JDZD071)。
作者简介:
陶祥兴, 数学博士, 浙江科技学院理学院教授, 博士生导师; 杨峥, 浙江科技学院理学院硕士研究生; 季彦颋, 哲学博士, 浙江科技学院理学院副教授。
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