Comparative Analysis of Classical and Time-Varying Lee–Carter Models for Mortality Forecasting in Indonesia and Japan
Abstract
Reliable mortality forecasting is essential for demographic planning and actuarial decision-making. This study compared the forecasting performance of the Classical and Time-Varying Lee–Carter models using World Population Prospects (WPP) 2024 mortality data for Indonesia and Japan (1970–2023). Both models were estimated using 1970–2015 data and evaluated on 2016–2023 through out-of-sample validation based on MAE, RMSE, and MAPE. For Indonesia, the Time-Varying model yielded a slightly lower MAPE (7.262%) than the Classical model (8.086%), whereas the Classical model produced slightly lower forecasting errors for Japan. Overall, the differences between the models were modest. The findings suggest that, in this study, forecasting performance was associated more closely with population-specific mortality characteristics than with model complexity alone.
Keywords
References
R. Duerst, S. Jonas, and C. Bohk-Ewald, “A Validation Workflow for Mortality Forecasting,” Rostock, Germany, WP-2023-020, 2023. https://doi.org/10.4054/MPIDR-WP-2023-020 .
A. Nalmpatian, C. Heumann, and S. Pilz, “Forecasting Mortality Trends: Advanced Techniques and the Impact of COVID-19,” Stats, vol. 7, no. 4, pp. 1172–1188, 2024, https://doi.org/10.3390/stats7040069.
D. Atance, M. Mercè Claramunt, X. Varea, and J. M. Aburto, “Convergence and divergence in mortality: A global study from 1990 to 2030,” PLoS ONE, vol. 19, no. 1, pp. 1–25, 2024, https://doi.org/10.1371/journal.pone.0295842.
United Nations, “World Population Prospects 2024: Methodology of the United Nations population estimates and projections,” New York, 2024.
L. De Mori, S. Haberman, P. Millossovich, and R. Zhu, “Mortality Forecasting via Multi-Task Neural Networks,” ASTIN Bulletin, vol. 55, no. 2, pp. 313–331, 2025, https://doi.org/10.1017/asb.2025.10.
J. Wakefield and V. Knutson, “Excess Mortality Estimation,” Annual Review of Statistics and Its Application, vol. 12, no. 1, pp. 45–68, 2025, https://doi.org/10.1146/annurev-statistics-112723-034236.
R. D. Lee and L. R. Carter, “Modeling and Forecasting U.S. Mortality,” Journal of the American Statistical Association, vol. 87, no. 419, pp. 659–671, 1992, https://doi.org/10.1080/01621459.1992.10475265.
U. Basellini, C. G. Camarda, and H. Booth, “Thirty years on: A review of the Lee–Carter method for forecasting mortality,” International Journal of Forecasting, vol. 39, no. 3, pp. 1033–1049, 2023, https://doi.org/10.1016/j.ijforecast.2022.11.002.
Fitriani, H. Cipta, and Rina Widyasari, “Penerapan Model Lee-Carter untuk Peramalan Angka Harapan Hidup Berdasarkan Usia di Kota Medan,” Leibniz: Jurnal Matematika, vol. 5, no. 02, pp. 129–140, 2025, https://doi.org/10.59632/leibniz.v5i02.509.
R. A. L. Kafi and A. A. Sihombing, “The comparison of random walk with drift and SES in forecasting Indonesian mortality rate with Lee-Carter model,” Jurnal Riset dan Aplikasi Matematika (JRAM), vol. 06, no. 01, pp. 73–79, 2022, https://doi.org/10.26740/jram.v6n1.p73-79.
Z. P. C. Kertayanda, T. Yulita, D. T. Julianty, A. Ginting, and M. N. A. Simanjuntak, “Life Table Prediction Using the Lee-Carter Model,” Journal of Actuarial, Finance and Risk Management (JAFRM), vol. 3, no. 1, 2024, https://doi.org/10.33021/jafrm.v3i1.5429.
A. U. Shelleng, H. G. Dikko, J. Garba, and B. B. Alhaji, “Assessing the suitability of the Lee-Carter model in modelling mortality data with varying bx parameter,” Fudma Journal of Sciences, vol. 7, no. 3, pp. 293–296, 2023, https://doi.org/10.33003/fjs-2023-0703-1874.
F. Novkaniza, R. Syach, and M. Novita, “Modified Lee–Carter Model Using Extreme Value Theory for Forecasting Mortality Rates Amidst Extreme Events During COVID-19 Era in Indonesia,” Communications in Mathematical Biology and Neuroscience, pp. 1–15, 2024, doi: 10.28919/cmbn/8656.
S. Tang, J. Li, and L. Tickle, “A New Fourier Approach under the Lee-Carter Model for Incorporating Time-Varying Age Patterns of Structural Changes,” Risks, vol. 10, no. 8, 2022, https://doi.org/10.3390/risks10080147.
L. He, F. Huang, J. Shi, and Y. Yang, “Mortality Forecasting using Factor Models: Time-varying or Time-invariant Factor Loadings?,” Insurance: Mathematics and Economics, vol. 98, pp. 1–40, 2021, https://doi.org/10.1016/j.insmatheco.2021.01.006.
S. A. Gyamerah, A. A. Mensah, C. Asare, and N. Dzupire, “Improving mortality forecasting using a hybrid of Lee–Carter and stacking ensemble model,” Bulletin of the National Research Centre, vol. 47, no. 1, 2023, https://doi.org/10.1186/s42269-023-01138-2.
J. Garrido, Y. Shang, and R. Xu, “LSTM-Based Coherent Mortality Forecasting for Developing Countries,” Risks, vol. 12, no. 2, pp. 1–24, 2024, https://doi.org/10.3390/risks12020027.
M. C. Fung, G. W. Peters, and P. V. Shevchenko, “A State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricing,” in Proceedings of the 21st International Congress on Modelling and Simulation (MODSIM2015), Gold Coast, Australia: Modelling and Simulation Society of Australia and New Zealand, 2015, pp. 952–958. https://doi.org/10.2139/ssrn.2699624.
M. Matějka and I. Malá, “The Usage of State Space Models in Mortality Modeling and Predictions,” Statistika, vol. 103, no. 1, pp. 121–131, 2023, https://doi.org/10.54694/STAT.2022.33.
R. Li, R. Zhou, and D. Pitt, “Dynamic Mortality Forecasting via Mixed-Frequency State-Space Models,” 2026.
Z. Chen, Y. Shi, and A. Shu, “Managing Mortality and Aging Risks with a Time-Varying Lee–Carter Model,” Healthcare (Switzerland), vol. 11, no. 5, pp. 1–20, 2023, https://doi.org/10.3390/healthcare11050743.
B. Koichubekov, B. Omarkulov, M. Mukhanova, and R. Zakirova, “Age-Specific Mortality Forecasting in Kazakhstan: Alternative Approaches to the Lee – Carter Model,” International Journal of Environmental Research and Public Health, vol. 22, no. 3, p. 346, 2025, https://doi.org/10.3390/ijerph22030346.
N. Redzwan, P. Sivasundaram, and R. Ramli, “Mortality Index Simulation for Forecasting Malaysian Mortality Rates,” ASM Science Journal, vol. 18, pp. 1–11, 2023, https://doi.org/10.32802/asmscj.2023.1465.
S. Sahin and S. Ozen, “A Quantitative Comparison of Mortality Models with Jumps: Pre- and Post-COVID Insights on Insurance Pricing,” Risks, vol. 12, no. 3, p. 53, 2024, https://doi.org/10.3390/risks12030053.
GBD 2021 Japan Collaborators, “Three decades of population health changes in Japan, 1990–2021: a subnational analysis for the Global Burden of Disease Study 2021,” The Lancet Public Health, vol. 10, no. 4, pp. e321–e332, 2025, https://doi.org/10.1016/S2468-2667(25)00044-1.
H. Surendra, D. Paramita, N. N. Arista, A. I. Putri, and A. A. Siregar, “Geographical variations and district-level factors associated with COVID-19 mortality in Indonesia: a nationwide ecological study,” BMC Public Health, pp. 1–12, 2023, https://doi.org/10.1186/s12889-023-15015-0.
C. T. Pallari et al., “Magnitude and determinants of excess total, age-specific and sex-specific all-cause mortality in 24 countries worldwide during 2020 and 2021: results on the impact of the COVID-19 pandemic from the C-MOR project,” BMJ Global Health, vol. 9, no. 4, 2024, https://doi.org/10.1136/bmjgh-2023-013018.
J. Durbin and S. J. Koopman, Time Series Analysis by State Space Methods, 2nd ed. Oxford: Oxford University Press, 2012. https://doi.org/10.1093/acprof:oso/9780199641178.001.0001.
R. E. Kalman, “A New Approach to Linear Filtering and Prediction Problems,” Journal of Basic Engineering, vol. 82, no. 1, pp. 35–45, 1960, https://doi.org/10.1115/1.3662552.
J. Helske, “KFAS: Exponential Family State Space Models in R,” Journal of Statistical Software, vol. 78, no. 10, pp. 1–39, 2017, https://doi.org/10.18637/jss.v078.i10.
A. Léger and S. Rizzi, “Month-to-month all-cause mortality forecasting: a method allowing for changes in seasonal patterns,” American Journal of Epidemiology, vol. 193, no. 6, pp. 898–907, 2024, https://doi.org/10.1093/aje/kwae004.
R. J. Hyndman and A. B. Koehler, “Another look at measures of forecast accuracy,” International Journal of Forecasting, vol. 22, no. 4, pp. 679–688, 2006, https://doi.org/10.1016/j.ijforecast.2006.03.001.
E. Strøm and O. E. Gundersen, “Performance metrics for multi-step forecasting measuring win-loss, seasonal variance and forecast stability: an empirical study,” Applied Intelligence, vol. 54, no. 13, pp. 10490–10515, 2024, https://doi.org/10.1007/s10489-024-05715-4.
P. Manandhar, H. Rafiq, E. Rodriguez-Ubinas, and T. Palpanas, “New Forecasting Metrics Evaluated in Prophet, Random Forest, and Long Short-Term Memory Models for Load Forecasting,” Energies, vol. 17, no. 14, pp. 1–30, 2024, https://doi.org/10.3390/en17143472.
Z. Pala and F. Şevgin, “Statistical Modeling for Long-Term Meteorological Forecasting: A Case Study in Van Lake Basin,” Natural Hazards, vol. 120, no. 12, pp. 14101–14116, 2024, https://doi.org/10.1007/s11069-024-06747-2.
F. X. Diebold and R. S. Mariano, “Comparing Predictive Accuracy,” Journal of Business & Economic Statistics, vol. 13, no. 3, pp. 253–263, 1995, https://doi.org/10.1080/07350015.1995.10524599.
DOI: http://dx.doi.org/10.30829/zero.v10i2.31283
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