Stochastic life table forecasting: A time-simultaneous fan chart application

Abstract

Given a fitted stochastic mortality model, we can express the uncertainty associated with future death rates in terms of confidence or prediction intervals. Recently, a group of researchers have proposed using fan charts to display prediction intervals for future mortality rates. Existing mortality fan charts are based on isolated pointwise prediction intervals. By pointwise we mean that the interval reflects uncertainty in a quantity at a single point of time, but it does not account for any dynamic property of the time-series. In this paper, we overcome this limitation by introducing the concept of time-simultaneous fan charts. In more detail, instead of pointwise intervals, a time-simultaneous fan chart is derived from a prediction band with a prescribed probability of covering the whole time trajectory. We present two numerical methods for producing time-simultaneous fan charts. These methods can be applied to common stochastic mortality models, including the generalized Cairns–Blake–Dowd model. Finally, the proposed method is illustrated with mortality data from the populations of Australia and New Zealand.