Compositional data analysis for modelling and forecasting mortality using the α-transformation

Mortality forecasting plays a central role in both demographic and actuarial studies. Classical approaches, such as the Lee-Carter (LC) model, typically rely on mortality rates as the primary measure. In recent years, compositional data analysis (CoDA), which respects summability and non-negativity constraints, has gained increasing attention for mortality forecasting. While the centred log-ratio (CLR) transformation is commonly used to map compositional data to real space, the α-transformation, a generalisation of log-ratio transformations, offers greater flexibility and adaptability. This study introduces the α-transformation as an alternative to the CLR transformation within a CoDA framework under a discrete-age setting for all-cause mortality forecasting, which has not been previously investigated. To enable a fair comparison of transformation choices, zero values in the data are imputed, although the α-transformation can inherently accommodate them. Using age-specific life table death counts for males and females in 31 selected European countries/regions from 1983 to 2018, the proposed method demonstrates comparable performance to the CLR transformation in most cases, with improved forecast accuracy in some instances. These findings highlight the potential of the α-transformation to enhance mortality forecasting within the CoDA framework.