Forecasting age distribution of life-table death counts via α-transformation

Abstract

We introduce a compositional power transformation, known as an {\alpha}-transformation, to model and forecast a time series of life-table death counts, possibly with zero counts observed at older ages. As a generalisation of the isometric log-ratio transformation (i.e., {\alpha} = 0), the {\alpha} transformation relies on the tuning parameter {\alpha}, which can be determined in a data-driven manner. Using the Australian age-specific period life-table death counts from 1921 to 2020, the {\alpha} transformation can produce more accurate short-term point and interval forecasts than the log-ratio transformation. The improved forecast accuracy of life-table death counts is of great importance to demographers and government planners for estimating survival probabilities and life expectancy and actuaries for determining annuity prices and reserves for various initial ages and maturity terms.