DOI QR코드

DOI QR Code

6-Parametric factor model with long short-term memory

  • Received : 2021.04.15
  • Accepted : 2021.08.27
  • Published : 2021.09.30

Abstract

As life expectancies increase continuously over the world, the accuracy of forecasting mortality is more and more important to maintain social systems in the aging era. Currently, the most popular model used is the Lee-Carter model but various studies have been conducted to improve this model with one of them being 6-parametric factor model (6-PFM) which is introduced in this paper. To this new model, long short-term memory (LSTM) and regularized LSTM are applied in addition to vector autoregression (VAR), which is a traditional time-series method. Forecasting accuracies of several models, including the LC model, 4-PFM, 5-PFM, and 3 6-PFM's, are compared by using the U.S. and Korea life-tables. The results show that 6-PFM forecasts better than the other models (LC model, 4-PFM, and 5-PFM). Among the three 6-PFMs studied, regularized LSTM performs better than the other two methods for most of the tests.

Keywords

References

  1. Azuma Y (2020). Core deep-learning introduction, SB Creative Corp.
  2. Booth H, Hyndman RJ, Tickle L, and De Jong P (2006). Lee-Carter mortality forecasting: A multi-country comparison of variants and extensions, Demographic Research, 15, 289-310. https://doi.org/10.4054/DemRes.2006.15.9
  3. Booth H, Maindonald J, and Smith L (2002). Applying Lee-Carter under conditions of variable mortality decline, Population Studies, 56, 325-336. https://doi.org/10.1080/00324720215935
  4. Booth H and Tickle L (2008). Mortality modelling and forecasting: A review of methods, Annals of Actuarial Science, 3, 3-43. https://doi.org/10.1017/S1748499500000440
  5. Cairns A, Blake D, and Dowd K (2006). A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration, The Journal of Risk and Insurance, 73, 687-718. https://doi.org/10.1111/j.1539-6975.2006.00195.x
  6. Choi J (2021). Comparison of accuracy between LC model and 4-parametric factor model when COVID-19 impacts mortality structure, Communications for Statistical Applications and Methods, 28, 233-250. https://doi.org/10.29220/CSAM.2021.28.3.233
  7. Chung J, Culcehre C, Cho K, and Bengio Y (2014). Empirical evaluation of gated recurrent neural networks on sequence modeling.
  8. Diebold FX and Li C (2006). Forecasting the term structure of government bond yields, Journal of Econometrics, 130, 337-364. https://doi.org/10.1016/j.jeconom.2005.03.005
  9. Gers F, Schmidhuber J, and Cummins F (2000). Learning to forget: continual prediction with LSTM, Neural Computation, 12, 2451-2471. https://doi.org/10.1162/089976600300015015
  10. Gompertz B (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies, Philosophical Transactions of the Royal Society of London, 115, 513-583. https://doi.org/10.1098/rstl.1825.0026
  11. Graves A, Mohamed A-r, and Hinton G (2013). Speech recognition with deep recurrent neural networks, IEEE International Conference on Acoustics, Speech, and Signal Processing.
  12. Haldrup N and Rosenskjold C (2019). Econometrics,
  13. Heligman L and Pollard JH (1980). The age pattern of mortality, Journal of the Institute of Actuaries, 107, 49-80. https://doi.org/10.1017/S0020268100040257
  14. Hastie T, Tibshirani R, and Friedman J (2009). The elements of statistical learning: data mining, inference, and prediction, Springer Series in Statistics.
  15. Hochreiter, Sepp and Schmidhuber, Jurgen (1997), long short-term memory, Neural Computation, 9, 1735-1780. https://doi.org/10.1162/neco.1997.9.8.1735
  16. Human mortality data, Retrieved from Dec 31, 2020, https://www.mortality.org/
  17. Hyndman RJ and Ullah MDS (2007). Robust forecasting of mortality and fertility rates: a functional data approach, Computational Statistics and Data Analysis, 51, 4942-4956. https://doi.org/10.1016/j.csda.2006.07.028
  18. Jozefowicz R, Zaremba W and Sutskever L (2015). An empirical exploration of recurrent network architectures. In Proceedings of ICML, 2342-2350.
  19. Lee RD and Carter LR (1992). Modeling and forecasting U.S. mortality, Journal of the American Statistical Association, 87, 659-671. https://doi.org/10.2307/2290201
  20. Li Nan and Lee R (2005). Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 42, 575-594. https://doi.org/10.1353/dem.2005.0021
  21. Merity S, Keskar NS, and Socher R (2017). Regularizing and optimizing LSTM language models.
  22. Nigri A, Levantesi S, Marino M, Scognamiglio S, and Perla F (2019). A deep learning integrated Lee-Carter model, Risks, 7.
  23. Perla F, Richman R, Scognamiglio S, and Wuthrich M (2021). Time-Series Forecasting of Mortality Rates using Deep Learning, Scandinavian Actuarial Journal, 2021, 572-598. https://doi.org/10.1080/03461238.2020.1867232
  24. Pfaff B (2008). VAR, SVAR, and SVEC Models: implementation within R Package vars, Journal of Statistical Software, 27, 1-32. https://doi.org/10.18637/jss.v027.i04
  25. Raschka S and Mirjalili V (2017). Python machine learning(2nd ed.), Packt Publishing.
  26. Renshaw AE and Haberman S (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: Mathematics and Economics, 38, 556-570. https://doi.org/10.1016/j.insmatheco.2005.12.001
  27. Richman R and Wuthrich MV (2019). Lee and Carter go machine learning: recurrent neural networks.
  28. Rogers A, and Little JS (1994). Parameterizing age patterns of demographic rates with the multiexponential model schedule, Mathematical Population Studies, 4, 175-195. https://doi.org/10.1080/08898489409525372
  29. Siler W (1979). A competing-risk model for animal mortality, Ecology, 60, 750-757. https://doi.org/10.2307/1936612
  30. Srivastava N, Hinton G, Krizhevsky A, Sutskever I, and Salakhutdinov R (2014). Dropout: a simple way to prevent neural networks from overfitting, Journal of Machine Learning Rresearch, 15, 1929-1958.
  31. Statistics Korea. Life-table, Retrieved from Dec 31, 2020, https://kosis.kr/statisticsList/statisticsListIndex.do?vwcd=MTZTITLE&menuId=M_01_01#content-group
  32. United Nations (2019), World Population Prospects 2019, Retrieved from Apr 01, 2021, http://population.un.org/wpp
  33. Wisniowski A, Smith PWF, Bijak J, Raymer J, and Forster JJ (2015), Bayesian population forecasting: extending the Lee Carter method, Demography, 52, 1035-1059. https://doi.org/10.1007/s13524-015-0389-y