Age-coherent extensions of the Lee–Carter model

Age coherence describes the property that forecast mortality rates across ages will not diverge in the long run. Although intuitively and biologically reasonable, this property is lost when the seminal Lee–Carter (LC) model and almost all its existing extensions are employed. In this paper, we propose two effective extensions of the LC model, allowing for the geometric (LC-G) and hyperbolic (LC-H) decayed relative speed of mortality decline at each age, over the out-of-sample forecasting steps. Those approaches are based on the original in-sample estimates of LC, which are easy to obtain. An inversed Epanechnikov kernel is employed to model the geometric and hyperbolic parameters across ages, and unknown parameters are selected via a data-driven method. With little added computational cost to LC, our approaches incorporate the dynamic and rotating relative speeds of mortality decline over ages, recognize the growing difficulty of such declines at older ages, provide age-coherent forecasts of mortality rates in the long run, and is easily extensible to multi-population cases. Using a large sample of 15 countries, we demonstrate that LC-G and LC-H, as well as their multi-population counterparties, consistently improve the forecasting accuracy of the competing LC model and its single- and multi-population extensions.Feng, L., Shi, Y., & Chang, L. (2021). Forecasting mortality with a hyperbolic spatial temporal VAR model. International Journal of Forecasting, 37(1), 255–273.