Mortality Models Incorporating Long Memory Improves Life Table Estimation: A Comprehensive Analysis

122 Pages Posted: 31 Mar 2018

See all articles by Hongxuan Yan

Hongxuan Yan

The University of Sydney - School of Mathematics and Statistics

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Jennifer Chan

The University of Sydney - School of Mathematics and Statistics

Date Written: March 26, 2018

Abstract

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.

Keywords: Life Table, Life Expectancy, Lee Carter Model, Fractional Integrated Model, Bayesian Inference

Suggested Citation

Yan, Hongxuan and Peters, Gareth and Chan, Jennifer, Mortality Models Incorporating Long Memory Improves Life Table Estimation: A Comprehensive Analysis (March 26, 2018). Available at SSRN: https://ssrn.com/abstract=3149914 or http://dx.doi.org/10.2139/ssrn.3149914

Hongxuan Yan

The University of Sydney - School of Mathematics and Statistics ( email )

Sydney, New South Wales 2006
Australia

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Jennifer Chan

The University of Sydney - School of Mathematics and Statistics ( email )

Sydney, New South Wales 2006
Australia

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