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

Han Ying Lim, Dharini Pathmanathan, Sophie Dabo-Niang

TL;DR

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.

Abstract

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.

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

TL;DR

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.

Abstract

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.
Paper Structure (16 sections, 7 equations, 4 figures, 3 tables)

This paper contains 16 sections, 7 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Data preprocessing
  4. The CLR transformation
  5. The $\alpha$-transformation
  6. Modelling and forecasting
  7. Model evaluation
  8. Application to real data
  9. $\alpha$-parameter tuning
  10. Forecasts of mortality: A case study on Italian female mortality
  11. Comparison of mean forecast accuracy
  12. Overall mean errors
  13. Mean errors by country/region
  14. Mean errors over years
  15. Mean errors by age
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Forecasted age-specific life table death counts (a) in 2018 and (b) for selected ages, with forecast errors (c) over years and (d) by ages for Italian females.
  • Figure 2: Mean forecast errors of the best ARIMA models for female mortality in each country/region. Asterisks (*) indicate cases where optimal $\alpha = 0$.
  • Figure 3: Mean forecast errors for female mortality over years across countries/regions.
  • Figure 4: Mean forecast errors for female mortality by age across countries/regions.