A New Fourier Approach under the Lee-Carter Model for Incorporating Time-Varying Age Patterns of Structural Changes

Abstract

The prediction of future mortality improvements is of substantial importance for areas such as population projection, government welfare policies, pension planning and annuity pricing. The Lee-Carter model is one of the widely applied mortality models proposed to capture and predict the trend in mortality reductions. However, some studies have identified the presence of structural changes in historical mortality data, which makes the forecasting performance of mortality models sensitive to the calibration period. Although some attention has been paid to investigating the time or period effects of structural shifts, the potential time-varying age patterns are often overlooked. This paper proposes a new approach that applies a Fourier series with time-varying parameters to the age sensitivity factor in the Lee-Carter model to study the evolution of age effects. Since modelling the age effects is separated from modelling the period effects, the proposed model can incorporate these two sources of structural changes into mortality predictions. Our backtesting results suggest that structural shifts are present not only in the Lee-Carter mortality index over time, but also in the sensitivity to those time variations at different ages.