Using The Lee-Carter Method To Forecast Urban China Mortality

The global aging's trend of development is the longevity risk cause. Broadly said that the longevity risk will be refers to future average actual life is higher than the risk which the life expectancy will produce. The longevity to the humanity no doubt is a good deed, but it simultaneously is also one kind of risk. With more and more long along with the life, the people are often insufficient in. the young time agglomeration's wealth to make up the expenditure in the old time. It is very difficult to achieve the support. It will be the important hindrance for our country economy steady progression in the future. So we should have a good method to forecast mortality rates.In 1992, Lee and Carter presented a new method to modelling and forecasting age-specific mortality rates, which combines a demographic model with a statistical model of time series. Originally applied to USA mortality data, the Lee-Carter method has gained importance mainly because of the quality of its empirical results and has been applied to data for several countries.In this paper we investigate the feasibility of using the Lee-Carter methodology to construct mortality forecasts for the urban population of China. We fit the model to the matrix of China death rates for each gender from 1996 to 2008. A time-varying index of mortality is forecasted in an ARIMA framework and is used to generate projected life tables. In particular we focus on life expectancies at birth and, for the purpose of comparison, we introduce an alternative approach for forecasting life expectancies on a period basis.There were two reasons for selecting the Lee-Carter model in our work. Firstly, this model represents one of the most influential recent developments in the field of mortality forecasts. Secondly, the important feature of this model is that for a precise value of the time index kt, we can define a complete set of death probabilities that allow us to calculate all of the life table. Once we estimate the parameters, depending on age{αx,βx}, they stay constant and invariant through time. Hence, when we know kt, we can use the parameters for any year of interest.The main contents of the dissertation are as following:Introduction entire chapter article structure which summarizes in this article first chapter of introduction, described this article research background as well as the research significance. In addition, it also has introduced domestic and foreign research situation of Lee-Carter methodology as well as the related literature internally.The second chapter described the Lee-Carter method for mortality projection and introduces the notation used in this paper. The LC model cannot be fitted by ordinary regression methods, because there are no given regressors, thus in order to find a least squares solution to the equation we use a close approximation, suggested by Lee and Carter, to the singular value decomposition (SVD) method, assuming that the errors are homoschedastic. Model fitting on China mortality data is illustrated, with particular attention to the re-estimation of kt.The third chapter began by employing a systematic outlier detection process to ascertain the timing, magnitude, and persistence of any outliers present in historical trends of the mortality index. We then try to match the identified outliers with important events that could possibly justify the vacillations in human mortality levels. At the same time, we adjust the effect of the outliers for model reestimation. The empirical results indicate that the outlier-adjusted model could achieve better fits and more efficient forecasts of variables such as the central rates of death and the life expectancies at birth.The fourth chapter, the estimated time-dependent parameter kt can be modelled as a stochastic process. We thus used the standard Box and Jenkins methodology to generate an appropriate ARIMA (p,d,q) model for the mortality index kt. Considering the time series given by the reestimated kt through chapter three and four. We need to identify a correct model, for our series, among the general class of ARIMA models. The procedure to construct the model goes through different iterative phases to arrive at a model that fits our data well.The fifth chapter, we forecast the mortality, and compare the death rate of 2009 from forecasting with the true so as to test the exact of our model.