Modern mortality forecasting follows two main traditions descended from Lee & Carter's seminal 1992 paper [1]. One decomposes age-by-time mortality into a few summary patterns and projects those patterns forward. The other models how fast life expectancy improves at each level of life expectancy. We argue that both can be viewed as restricted versions of a single underlying object: a smooth trajectory through a low-dimensional summary of mortality derived from a multi-way decomposition of the sex × age × country × year mortality array. The unrestricted version of this object is the flow-field forecaster. We compare it with the leading existing methods on the Human Mortality Database [6]: each method sees only the data up to the year its forecast starts. The results so far are encouraging.

How we compare forecasts

For 43 populations in the HMD, forecasts start every five years from 1900 to 2015 and run 50 years ahead. Twelve forecasters compete. The flow-field is one. MDMx, a companion forecaster built on the same decomposition, Lee–Carter [1], Hyndman & Ullah's functional-data model [2], Hyndman, Booth & Yasmeen's coherent functional model [13], and the bayesLife/MortCast pipeline [3, 4] that the United Nations uses for its mortality forecasts [5] make ten more, each fitted both to all past years and to the last 50 (bayesLife from its own Bayesian estimation at every start year). An equal-weight average of the flow-field, MDMx and Lee–Carter is the twelfth. A random walk with drift is the baseline.

A comprehensive comparison scores each forecaster on five features: life expectancy for each sex, the life expectancy gap between the sexes, the age-specific differences between the sexes, the age pattern of mortality (weighted by where deaths occur, with life expectancy at 65), and the calibration of interval forecasts. Every score measures the size of the errors, relative to the baseline, so over- and under-predictions cannot offset each other. The forecasters are ranked over 20,000 random weightings of the five aspects, each with a resampling of the populations, so that no single choice of weights decides the result. The main test uses the forecasts from 1955–2000 at 1–15 years ahead. The forecasts from 2005–2015 were held out of every modelling choice and scored once, at the end.

What we're seeing so far

From 1955–2000, at 1–15 years ahead, the flow-field ranks first in 90% of the 20,000 draws, ahead of the ensemble average (7%) and MDMx. Its error in life expectancy is 0.42 years at 1–5 years ahead and 0.97 years at 11–15, against 0.48 and 1.55 for the baseline, and it is the only forecaster that beats the baseline on every one of the nine measures. Its lead is clearest beyond five years ahead; at 1–5 years the ensemble is as accurate. On the held-out forecasts from 2005–2015 the flow-field keeps its lead, with an error of 0.25 years at 1–5 years ahead. Forecasts from the early twentieth century, outside today's regime of mortality decline, are a harder test: there the flow-field still ranks first, but in fewer than half of the draws (47%, ahead of the ensemble's 29%).

First (share of the draws ranked first) and rank (mean rank) come from the comprehensive comparison, for the forecasts from 1955–2000 at 1–15 years ahead. Errors are mean absolute errors in life expectancy at birth (the average of the two sexes), in years, at 1–5 and 11–15 years ahead. The held-out column scores the forecasts from 2005–2015, which no modelling choice used. Each method is shown fitted to the period that serves it better (all past years, or the last 50); the ensemble averages the flow-field, MDMx and Lee–Carter; the random walk with drift is the baseline, not a competitor.

NB: The numerical results presented here are preliminary, drawn from a manuscript in preparation. They can shift as the evaluation is refined and as the comparisons receive external scrutiny. Treat what's reported here as a research preview rather than a settled comparison.

References & further reading

1. Lee, R. D. & Carter, L. R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association 87(419): 659–671. doi:10.1080/01621459.1992.10475265
2. Hyndman, R. J. & Ullah, M. S. (2007). Robust forecasting of mortality and fertility rates: A functional data approach. Computational Statistics & Data Analysis 51(10): 4942–4956. doi:10.1016/j.csda.2006.07.028
3. Raftery, A. E., Chunn, J. L., Gerland, P. & Ševčíková, H. (2013). Bayesian probabilistic projections of life expectancy for all countries. Demography 50(3): 777–801. doi:10.1007/s13524-012-0193-x
4. Ševčíková, H., Li, N., Kantorová, V., Gerland, P. & Raftery, A. E. (2016). Age-specific mortality and fertility rates for probabilistic population projections. In R. Schoen (Ed.), Dynamic Demographic Analysis, pp. 285–310. Springer. doi:10.1007/978-3-319-26603-9_15
5. United Nations, Department of Economic and Social Affairs, Population Division (2024). World Population Prospects 2024: Methodology of the United Nations population estimates and projections. UN DESA/POP/2024/DC/NO.10. population.un.org/wpp/.../WPP2024_Methodology-Report_Final.pdf
6. Human Mortality Database (2026). Max Planck Institute for Demographic Research (Germany), University of California, Berkeley (USA), and French Institute for Demographic Studies (France). www.mortality.org
7. Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika 31(3): 279–311. doi:10.1007/BF02289464
8. Li, N. & Lee, R. (2005). Coherent mortality forecasts for a group of populations: An extension of the Lee–Carter method. Demography 42(3): 575–594. doi:10.1353/dem.2005.0021
9. Li, N., Lee, R. & Gerland, P. (2013). Extending the Lee–Carter method to model the rotation of age patterns of mortality decline for long-term projections. Demography 50(6): 2037–2051. doi:10.1007/s13524-013-0232-2
10. Raftery, A. E., Lalic, N. & Gerland, P. (2014). Joint probabilistic projection of female and male life expectancy. Demographic Research 30(27): 795–822. doi:10.4054/DemRes.2014.30.27
11. Fosdick, B. K. & Hoff, P. D. (2014). Separable factor analysis with applications to mortality data. Annals of Applied Statistics 8(1): 120–147. doi:10.1214/13-AOAS694
12. Basellini, U., Camarda, C. G. & Booth, H. (2023). Thirty years on: A review of the Lee–Carter method for forecasting mortality. International Journal of Forecasting 39(3): 1033–1049. doi:10.1016/j.ijforecast.2022.11.002
13. Hyndman, R. J., Booth, H. & Yasmeen, F. (2013). Coherent mortality forecasting: The product-ratio method with functional time series models. Demography 50(1): 261–283. doi:10.1007/s13524-012-0145-5