Forecasting mortality rates with the penalized exponential smoothing state space model

Yanlin Shi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
18 Downloads (Pure)


It is well known that accurate forecasts of mortality rates are essential to various demographic research like population projection, and the pricing of insurance products such as pensions and annuities. Recent studies suggest that mortality rates of multivariate ages are usually not leading indicators in mortality forecasting. Therefore, multivariate stochastic mortality models including the classic Lee–Carter may not necessarily lead to more accurate forecasts, compared with sophisticated univariate counterparties like the exponential smoothing state space (ETS) model. Despite its improved forecasting accuracy, the original ETS model cannot ensure the age-coherence of forecast mortality rates. By introducing an effective penalty scheme, we propose a penalized ETS model to significantly overcome this problem, with discussions on related technical issues including the reduction of parameter dimensionality and the selection of tuning parameter. Empirical results based on mortality rates of the Australian males and females suggest that the proposed model consistently outperforms the Lee–Carter and original ETS models. Robust conclusions are drawn when various forecasting scenarios are considered. Long-term forecasting analyses up to 2050 comparing the three models are further performed. To illustrate its usefulness in practice, an application to price fixed-term annuities with the penalized ETS model is demonstrated.

Original languageEnglish
Pages (from-to)955-968
Number of pages14
JournalJournal of the Operational Research Society
Issue number5
Early online date19 Mar 2021
Publication statusPublished - 4 May 2022


  • exponential smoothing
  • Lee–Carter model
  • Mortality forecasting
  • penalty scheme


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