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Mortality models incorporating long memory for life table estimation: a comprehensive analysis

Published online by Cambridge University Press:  02 February 2021

Hongxuan Yan ,
Gareth W. Peters  and
Jennifer Chan
Hongxuan Yan*
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing100190, China Center for Forecasting Science, Chinese Academy of Sciences, Beijing100190, China
Gareth W. Peters
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, EdinburghEH14 4AS, UK
Jennifer Chan
Affiliation:
School of Mathematics and Statistics, The University of Sydney, Sydney, 2006, Australia
*
*Corresponding author. E-mail: yhx19901122@gmail.com
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Abstract

Mortality projection and forecasting of life expectancy are two important aspects of the study of demography and life insurance modelling. We demonstrate in this work the existence of long memory in mortality data. Furthermore, models incorporating long memory structure provide a new approach to enhance mortality forecasts in terms of accuracy and reliability, which can improve the understanding of mortality. Novel mortality models are developed by extending the Lee–Carter (LC) model for death counts to incorporate a long memory time series structure. To link our extensions to existing actuarial work, we detail the relationship between the classical models of death counts developed under a Generalised Linear Model (GLM) formulation and the extensions we propose that are developed under an extension to the GLM framework known in time series literature as the Generalised Linear Autoregressive Moving Average (GLARMA) regression models. Bayesian inference is applied to estimate the model parameters. The Deviance Information Criterion (DIC) is evaluated to select between different LC model extensions of our proposed models in terms of both in-sample fits and out-of-sample forecasts performance. Furthermore, we compare our new models against existing models structures proposed in the literature when applied to the analysis of death count data sets from 16 countries divided according to genders and age groups. Estimates of mortality rates are applied to calculate life expectancies when constructing life tables. By comparing different life expectancy estimates, results show the LC model without the long memory component may provide underestimates of life expectancy, while the long memory model structure extensions reduce this effect. In summary, it is valuable to investigate how the long memory feature in mortality influences life expectancies in the construction of life tables.

Keywords

Life tableLife expectancyLee–Carter modelFractional integrated modelBayesian inferenceLong memoryGLARMA
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 15 , Issue 3 , November 2021 , pp. 567 - 604
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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