A Two-population extension of the exponential smoothing state space model with a smoothing penalisation scheme

Yanlin Shi, Sixian Tang, Jackie Li

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1 Citation (Scopus)
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The joint modelling of mortality rates for multiple populations has gained increasing popularity in areas such as government planning and insurance pricing. Sub-groups of a population often preserve similar mortality features with short-term deviations from the common trend. Recent studies indicate that the exponential smoothing state space (ETS) model can produce outstanding prediction performance, while it fails to guarantee the consistency across neighbouring ages. Apart from that, single-population models such as the famous Lee-Carter (LC) may produce divergent forecasts between different populations in the long run and thus lack the property of the so-called coherence. This study extends the original ETS model to a two-population version (2-ETS) and imposes a smoothing penalisation scheme to reduce inconsistency of forecasts across adjacent ages. The exponential smoothing parameters in the 2-ETS model are fitted by a Fourier functional form to reduce dimensionality and thus improve estimation efficiency. We evaluate the performance of the proposed model via an empirical study using Australian female and male population data. Our results demonstrate the superiority of the 2-ETS model over the LC and ETS as well as two multi-population methods - the augmented common factor model (LL) and coherent functional data model (CFDM) regarding forecast accuracy and coherence.
Original languageEnglish
Article number67
Pages (from-to)1-18
Number of pages18
Issue number3
Early online date29 Jun 2020
Publication statusPublished - Sep 2020

Bibliographical note

Copyright 2020 by the authors. Licensee MDPI, Basel, Switzerland. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • mortality forecasting
  • exponential smoothing
  • penalty scheme
  • coherent mortality models
  • Exponential smoothing
  • Coherent mortality models
  • Mortality forecasting
  • Penalty scheme


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