Forecasting life expectancy and mortality are two important aspects for the study of demography. We demonstrate in this work that the existence of long memory in mortality data improves the understanding of mortality and the model incorporating a long memory structure provides a new approach to enhance the mortality forecasts. To achieve this we first demonstrate the existence of long memory in mortality data using Hurst exponent estimated by several empirical estimation methods. Then the dynamic of the long memory across genders, age groups, countries and time periods is further analysed. Results motivate us to develop new mortality models by extending the Lee Carter model to death counts and incorporating a long memory model structure. Bayesian inference is applied to estimate the model parameters. The Deviance Information Criterion is evaluated to select between different Lee Carter model extensions of our proposed models in terms of both in-sample fits and out-of-sample forecasts performance. Then the models are applied to analyse death count data sets from 16 different countries divided according to genders and age groups. Estimates of mortality rates are applied to calculate life expectancies when constructing life tables. On comparing different life expectancy estimates, results show the Lee Carter model without the long memory component may provide underestimates of life expectancy. This underestimation has great impact on the old-age support programs in social security and pension and may eventually lead to insufficient funds in a pension scheme. In summary, it is crucial to investigate how the long memory feature in mortality influences life expectancies in the construction of life tables.
Yan, H., Peters, G., & Chan, J. (2018). Mortality Models Incorporating Long Memory Improves Life Table Estimation: A Comprehensive Analysis. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3149914