Mortality forecasting is crucial for demographic planning and actuarial studies, especially for projecting population ageing and longevity risk. Classical approaches largely rely on extrapolative methods, such as the Lee-Carter (LC) model, which use mortality rates as the mortality 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 contributes to mortality forecasting by introducing the α-transformation as an alternative to the CLR transformation within a non-functional CoDA model that has not been previously investigated in existing literature. To fairly compare the impact of transformation choices on forecast accuracy, zero values in the data are imputed, although the α-transformation can inherently handle 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 for enhancing mortality forecasting within the non-functional CoDA framework.

翻译：死亡率预测对于人口规划与精算研究至关重要，尤其在预测人口老龄化与长寿风险方面。经典方法主要依赖外推法，例如使用死亡率作为度量指标的Lee-Carter（LC）模型。近年来，遵循可加性和非负性约束的组合数据分析（CoDA）在死亡率预测领域受到越来越多的关注。虽然中心对数比（CLR）变换通常用于将组合数据映射至实数空间，但作为对数比变换推广形式的α变换提供了更高的灵活性与适应性。本研究通过将α变换作为CLR变换的替代方案引入一个现有文献尚未探讨的非函数型CoDA模型，为死亡率预测领域作出贡献。为公平比较变换选择对预测精度的影响，尽管α变换本身能够处理零值，本文仍对数据中的零值进行了插补。使用1983年至2018年间31个欧洲国家/地区分性别、分年龄的生命表死亡人数数据，所提方法在多数情况下表现出与CLR变换相当的预测性能，并在部分案例中实现了更高的预测精度。这些发现凸显了α变换在非函数型CoDA框架内提升死亡率预测能力的潜力。