Mortality Estimation Based On Change-point Detection Of Principal Component Scores

The advent of the Lee-Carter model(referred to as the classical LC model)is a milestone in the development of the stochastic mortality model.However,one of the defects of the classical LC model is that the variance of its random error term is heterogeneous,which increases the instability of the mortality prediction results.Based on the principal component analysis,the logarithmic center mortality regression model(referred to as the classical PC model)constructed with the main component score as explanatory variables makes the heteroscedasticity problem solved by increasing the number of principal components.However,the classical PC model holds two the problem hinders its development.First,the prediction of the principal component scores in the classical PC model.Second,the demographic significance of each principal component in the classical PC model is not clear.In this paper,two problems in the classical PC model are studied,the multiple change-point detection method is applied to the prediction of population mortality,and the demographic explanation of the main principal components of the fluctuation of mortality from its mean value is given.First,the principal component analysis was used to analyze the fluctuation of mortality from its mean value.Using the continuous 60 years mortality data from 1951 to 2010 in the developed countries,the classical LC model and the classical PC model are compared from three aspects.The results show that the classical LC model can be regarded as the case where the classical PC model only contains the first principal component.By increasing the number of principal components,the heteroscedasticity in the classical LC model can be reduced or eliminated.Secondly,the change-point detection method was used to estimate the optimal number of change points and the position of the change points in the piecewise linear regression of the main principal component scores,and then predicted values of the principal component scores were extrapolated according to the last regression model.Finally,the demographic significance of the first two principal components is given by combining the coefficients of the principal component scores and the mortality improvement heat chart.The results show that the multiple change-point detection method improves the prediction accuracy of the mortality model.And the first principal component of the fluctuation of mortality from its mean value mainly synthesizes the decreasing information on the mortality of all age groups with time,the second principal component mainly synthesizes the effect of cohort effect on mortality.