Lee-Carter死亡率模型中死亡率指数的单位根检验

发布时间：2018-04-18 21:51

本文选题：长寿风险 + 死亡率　；参考：《中国科学技术大学》2016年博士论文

【摘要】：长寿风险是指个人或总体人群未来的平均实际寿命高于预期寿命所产生的风险.在过去几十年中,人类预期寿命已大大增加.为了成功对冲长寿风险,正确理解与精确预测死亡率趋势是至关重要的Lee Carter于1992年提出了一种外推方法用来建模和预测美国死亡率模型.目前,该方法已被广泛应用于预测不同年龄段的死亡率,成为文献中寿命预测的标准模型.该Lee-Carter死亡率模型涉及两步估计过程.在对Lee-Carter及其扩展模型进行实证研究时,随机游动模型(ARIMA(0,1,0))被挑选用来建模死亡率指数随时间变化的趋势.其中,死亡率指数在死亡率预测与长寿风险管理上起决定作用.本文首次证明了当死亡率指数kt不是一单位根过程时,Lee-Carter死亡率模型的两步推断过程是不相合的.随后,我们给出了检验kt是否是单位根过程的方法,并对1933年-2010年美国死亡率数据做检验.其结果拒绝了零假设,即我们不认为美国死亡率指数kt服从单位根过程.这就呼吁相关人员要谨慎应用Lee-Carter死亡率模型及其扩展模型.另一方面,我们首次将加权连接方程应用在Qin Lawless (1994)提出的经验似然方法中,从而给出了伴随有平稳GARCH误差的一阶自回归过程与带漂移项的一阶自回归过程的一致单位根检验方法.这里,一致是不依赖于GARCH误差的矩条件或其重尾特征.通常情况下,我们很难得到GARCH误差尾指数的显示解,故一致检验是极为必要的.
[Abstract]:Longevity risk refers to the individual or the general population future average actual life is higher than life expectancy generated. In the past few decades, life expectancy has increased greatly. In order to successfully hedge longevity risk, correct understanding and accurate prediction of mortality trends is essential to Lee Carter in 1992 proposed an extrapolation method is used to modeling and forecasting the United States mortality model. At present, this method has been widely used in the prediction of different age mortality, become the standard model in the literature and life. The mortality of Lee-Carter model involves two steps estimation process. In the empirical research on Lee-Carter and its extension model, random walk model (ARIMA (0,1,0)) were chosen for modeling mortality index trends over time. Among them, the mortality index plays a decisive role in predicting mortality and longevity risk management for the first time. Prove that when the mortality index KT is not a unit root process, the two step process of inference of Lee-Carter mortality model is not consistent. Then, we give the test whether KT is a method of unit root process, and in 1933 the United States -2010 test. Results the mortality data do reject the null hypothesis, that we don't think the mortality index KT follows a unit root process. This will appeal to the relevant personnel should be cautious application of the mortality of Lee-Carter model and its extended model. On the other hand, we will be the first application on Qin Lawless weighted connection equation (1994) put forward the experience of likelihood method, which gives a consistent unit of first-order stationary GARCH error autoregressive process with a first-order autoregressive process with drift root test. Here is consistent with that moment conditions do not depend on the GARCH error or heavy tailed characteristics. Usually, it is difficult for us to It is very necessary to obtain the display solution of the GARCH error tail exponent, so the uniform test is very necessary.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O212.1

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