  Many existing mortality models follow the framework of classical factor
models, such as the Lee-Carter model and its variants. Latent common factors in
factor models are defined as time-related mortality indices (such as $\kappa_t$
in the Lee-Carter model). Factor loadings, which capture the linear
relationship between age variables and latent common factors (such as $\beta_x$
in the Lee-Carter model), are assumed to be time-invariant in the classical
framework. This assumption is usually too restrictive in reality as mortality
datasets typically span a long period of time. Driving forces such as medical
improvement of certain diseases, environmental changes and technological
progress may significantly influence the relationship of different variables.
In this paper, we first develop a factor model with time-varying factor
loadings (time-varying factor model) as an extension of the classical factor
model for mortality modelling. Two forecasting methods to extrapolate the
factor loadings, the local regression method and the naive method, are proposed
for the time-varying factor model. From the empirical data analysis, we find
that the new model can capture the empirical feature of time-varying factor
loadings and improve mortality forecasting over different horizons and
countries. Further, we propose a novel approach based on change point analysis
to estimate the optimal `boundary' between short-term and long-term
forecasting, which is favoured by the local linear regression and naive method,
respectively. Additionally, simulation studies are provided to show the
performance of the time-varying factor model under various scenarios.
