Skip to main content
SpringerLink
Log in

Backtesting Recurrent Neural Networks with Gated Recurrent Unit: Probing with Chilean Mortality Data

  • Conference paper
  • First Online:
Advances and Applications in Computer Science, Electronics, and Industrial Engineering (CSEI 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 433))

Abstract

Understanding the survival prospects of a given population is essential in multiple research and policy areas, including public and private health care and social care, demographic analysis, pension systems evaluation, the valuation of life insurance and retirement income contracts, and the pricing and risk management of novel longevity-linked capital market instruments. This paper conducts a backtesting analysis to assess the predictive performance of Recurrent Neural Networks (RNN) with Gated Recurrent Unit (GRU) architecture in modelling and multivariate time series forecasting of age-specific mortality rates on Chilean mortality data. We investigate the best specification for one, two, and three hidden layers GRU networks and compare the RNN’s forecasting accuracy with that produced by principal component methods, namely a Regularized Singular Value Decomposition (RSVD) model. The empirical results suggest that the forecasting accuracy of RNN models critically depends on hyperparameter calibration and that the two hidden layer RNN-GRU networks outperform the RSVD model. RNNs can generate mortality schedules that are biologically plausible and fit well the mortality schedules across age and time. However, further investigation is necessary to confirm the superiority of deep learning methods in forecasting human survival across different populations and periods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For some examples on the joint modelling of both sexes’ mortality schedules see, e.g., Hyndman et al. [31], Richman and Wüthrich [34] and Bravo [11].

  2. 2.

    Due to space constraints, the results for the male population are not included in the main manuscript but are available from the authors upon request.

References

  1. Alho J, Bravo JM, Palmer E (2013). Annuities and life expectancy in NDC. In: Holzmann R, Palmer E, Robalino D (eds) Nonfinancial defined contribution pension schemes in a changing pension world, vol 2. Gender, Politics, and Financial Stability. World Bank Publications, pp 395–436. https://doi.org/10.1596/9780821394786_CH22

  2. Ashofteh A, Bravo JM (2020) A study on the quality of Novel Coronavirus (Covid-19) official datasets. Stat J IAOS 36(2):291–301. https://doi.org/10.3233/SJI-200674

    Article  Google Scholar 

  3. Ashofteh A, Bravo JM (2021) Life table forecasting in COVID-19 times: an ensemble learning approach. In: CISTI 2021 - 16th Iberian conference on information systems and technologies, pp 1–6. https://doi.org/10.23919/CISTI52073.2021.9476583

  4. Ayuso M, Bravo JM, Holzmann R (2021) Getting life expectancy estimates right for pension policy: period versus cohort approach. J Pension Econ Finance 20(2):212–231. https://doi.org/10.1017/S1474747220000050

    Article  Google Scholar 

  5. Ayuso M, Bravo JM, Holzmann R, Palmer E (2021) Automatic indexation of pension age to life expectancy: when policy design matters. Risks 9(5):96. https://doi.org/10.3390/risks9050096

    Article  Google Scholar 

  6. Blake D, Cairns AJG, Dowd K, Kessler AR (2019) Still living with mortality: the longevity risk transfer market after one decade. Br Actuar J 24:1–80

    Article  Google Scholar 

  7. Bravo JM (2016) Taxation of pensions in Portugal: a semi-dual income tax system. CESifo DICE Rep J Inst Comp 14(1):14–23

    Google Scholar 

  8. Bravo JM (2019) Funding for longer lives: retirement wallet and risk-sharing annuities. Ekonomiaz 96(2):268–291

    Google Scholar 

  9. Bravo JM (2021) Pricing participating longevity-linked life annuities: a Bayesian Model Ensemble approach. Eur Actuar J. https://doi.org/10.1007/s13385-021-00279-w

    Article  Google Scholar 

  10. Bravo JM (2021b) Pricing survivor bonds with affine-jump diffusion stochastic mortality models. In: 2021b the 5th international conference on E-commerce, E-business and E-government (ICEEG 2021). Association for Computing Machinery (ACM), New York, pp 91–96. https://doi.org/10.1145/3466029.3466037

  11. Bravo JM (2021c) Forecasting longevity for financial applications: a first experiment with deep learning methods. In: Kamp M et al (eds) Machine Learning and Principles and Practice of Knowledge Discovery in Databases. ECML PKDD 2021. Communications in Computer and Information Science, vol 1525. Springer, Cham. pp. 232–249. https://doi.org/10.1007/978-3-030-93733-1_17

  12. Bravo JM (2021d) Forecasting mortality rates with Recurrent Neural Networks: a preliminary investigation using Portuguese data. In: CAPSI 2021d proceedings (Atas da 21ª Conferência da Associação Portuguesa de Sistemas de Informação 2021), in press

    Google Scholar 

  13. Bravo JM, Ayuso M (2020) Mortality and life expectancy forecasts using Bayesian model combinations: an application to the Portuguese population. RISTI - Revista Ibérica de Sistemas e Tecnologias de Informação E40:128–144. https://doi.org/10.17013/risti.40.128-145

  14. Bravo JM, Ayuso M (2021a) Forecasting the retirement age: a Bayesian model ensemble approach. In: Advances in intelligent systems and computing, AIST, vol 1365. Springer, Cham, pp 123–135 [2021a World Conference on Information Systems and Technologies, WorldCIST 2021]. https://doi.org/10.1007/978-3-030-72657-7_12

  15. Bravo JM, Ayuso M (2021b) Linking pensions to life expectancy: tackling conceptual uncertainty through bayesian model averaging. Mathematics 9(24): 3307, p. 1-27. https://doi.org/10.3390/math9243307

  16. Bravo JM, El Mekkaoui de Freitas N (2018) Valuation of longevity-linked life annuities. Insur Math Econ 78:212–229

    Google Scholar 

  17. Bravo JM, Herce JA (2022) Career breaks, broken pensions? Long-run effects of early and late-career unemployment spells on pension entitlements. J Pension Econ Financ 21(2): 191–217.https://doi.org/10.1017/S1474747220000189

  18. Bravo JM, Nunes JPV (2021) Pricing longevity derivatives via Fourier transforms. Insur Math Econ 96:81–97

    Google Scholar 

  19. Bravo JM, Silva CM (2006) Immunization using a stochastic process independent multifactor model: the Portuguese experience. J Bank Finance 30(1):133–156

    Article  Google Scholar 

  20. Bravo JM, Ayuso M, Holzmann R, Palmer E (2021) Addressing the life expectancy gap in pension policy. Insur Math Econ 99:200–221. https://doi.org/10.1016/j.insmatheco.2021.03.025

  21. Chamboko R, Bravo JM (2016) On the modelling of prognosis from delinquency to normal performance on retail consumer loans. Risk Manage 18(4):264–287

    Article  Google Scholar 

  22. Chamboko R, Bravo JM (2020) A multi-state approach to modelling intermediate events and multiple mortgage loan outcomes. Risks 8:64

    Article  Google Scholar 

  23. Cho K, Van Merriënboer B, Bahdanau D, Bengio Y (2014) On the properties of neural machine translation: encoder-decoder approaches. arXiv preprint arXiv:1409.1259

  24. Coughlan GD, Epstein D, Honig P (2007) Q-forwards: derivatives for transferring longevity and mortality risks. Working paper. J. P. Morgan Pension Advisory Group, London

    Google Scholar 

  25. Deprez P, Shevchenko P, Wüthrich M (2017) Machine learning techniques for mortality modeling. Eur Actuar J 7:337–352

    Article  MathSciNet  Google Scholar 

  26. Dowd K, Cairns A, Blake D, Coughlan G, Epstein D, Khalaf-Allah M (2010) Backtesting stochastic mortality models. North Am Act J 14(3):281–298

    Article  Google Scholar 

  27. Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780

    Article  Google Scholar 

  28. Hong WH, Yap JH, Selvachandran G et al (2021) Forecasting mortality rates using hybrid Lee-Carter model, artificial neural network and random forest. Complex Intell Syst 7:163–189

    Article  Google Scholar 

  29. Huang JZ, Shen H, Buja A (2009) The analysis of two-way functional data using two-way regularized singular value decompositions. J Am Stat Assoc 104(488):1609–1620

    Article  MathSciNet  Google Scholar 

  30. Human Mortality Database (2021) University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany)

    Google Scholar 

  31. Hyndman RJ, Booth H, Yasmeen F (2013) Coherent mortality forecasting: the product-ratio method with functional time series models. Demography 50(1):261–283

    Article  Google Scholar 

  32. Kontis V, Bennett J, Mathers C, Li G, Foreman K, Ezzati M (2017) Future life expectancy in 35 industrialised countries: projections with a Bayesian model ensemble. Lancet 389(10076):1323–1335

    Article  Google Scholar 

  33. Lee RD, Carter L (1992) Modeling and forecasting U.S. mortality. J Am Stat Assoc 87:659–671

    MATH  Google Scholar 

  34. Richman R, Wüthrich M (2019) Lee and Carter go machine learning: recurrent neural networks. SSRN https://ssrn.com/abstract=3441030. Accessed 10 Jan 2021

  35. Simões C, Oliveira L, Bravo JM (2021) Immunization strategies for funding multiple inflation-linked retirement income benefits. Risks 9(4):60. https://doi.org/10.3390/risks9040060

  36. Zhang A, Lipton Z, Li M, Smola A (2021) Dive into deep learning. arXiv:2106.11342.

  37. Zhang L, Shen H, Huang JZ (2013) Robust regularized singular value decomposition with application to mortality data. Ann Appl Stat 7(3):1540–1561

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors express their gratitude to the editors and the anonymous referees for his or her careful review and insightful comments, which helped strengthen the quality of the paper. The authors were supported by Portuguese national funds through FCT under the project UIDB/04152/2020—Centro de Investigação em Gestão de Informação (MagIC) and grant UIDB/00315/2020 (BRU-ISCTE).

Author information

Authors and Affiliations

  1. Universidade Nova de Lisboa - NOVA IMS & Université Paris-Dauphine PSL & MagIC & CEFAGE-UE & BRU-ISCTE, Lisbon, Portugal

    Jorge M. Bravo

  2. Universidade Nova de Lisboa - NOVA IMS & MagIC, Lisbon, Portugal

    Vitor Santos

Authors
  1. Jorge M. Bravo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vitor Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jorge M. Bravo .

Editor information

Editors and Affiliations

  1. Universidad del País Vasco, Bilbao, Spain

    Marcelo V. Garcia

  2. FISEI, Universidad Técnica de Ambato, Ambato, Ecuador

    Félix Fernández-Peña

  3. FISEI, Universidad Técnica de Ambato, Ambato, Ecuador

    Carlos Gordón-Gallegos

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bravo, J.M., Santos, V. (2022). Backtesting Recurrent Neural Networks with Gated Recurrent Unit: Probing with Chilean Mortality Data. In: Garcia, M.V., Fernández-Peña, F., Gordón-Gallegos, C. (eds) Advances and Applications in Computer Science, Electronics, and Industrial Engineering. CSEI 2021. Lecture Notes in Networks and Systems, vol 433. Springer, Cham. https://doi.org/10.1007/978-3-030-97719-1_9

Download citation

Publish with us

Policies and ethics

Search

Navigation