Time-simultaneous prediction bands: A new look at the uncertainty involved in forecasting mortality

Conventionally, isolated (point-wise) prediction intervals are used to quantify the uncertainty in future mortality rates and other demographic quantities such as life expectancy. A pointwise interval reflects uncertainty in a variable at a single time point, but it does not account for any dynamic property of the time-series. As a result, in situations when the path or trajectory of future mortality rates is important, a band of pointwise intervals might lead to an invalid inference. To improve the communication of uncertainty, a simultaneous prediction band can be used. The primary objective of this paper is to demonstrate how simultaneous prediction bands can be created for prevalent stochastic models, including the Cairns-Blake-Dowd and Lee-Carter models. The illustrations in this paper are based on mortality data from the general population of England and Wales.