  Modelling and forecasting homogeneous age-specific mortality rates of
multiple countries could lead to improvements in long-term forecasting. Data
fed into joint models are often grouped according to nominal attributes, such
as geographic regions, ethnic groups, and socioeconomic status, which may still
contain heterogeneity and deteriorate the forecast results. Our paper proposes
a novel clustering technique to pursue homogeneity among multiple functional
time series based on functional panel data modelling to address this issue.
Using a functional panel data model with fixed effects, we can extract common
functional time series features. These common features could be decomposed into
two components: the functional time trend and the mode of variations of
functions (functional pattern). The functional time trend reflects the dynamics
across time, while the functional pattern captures the fluctuations within
curves. The proposed clustering method searches for homogeneous age-specific
mortality rates of multiple countries by accounting for both the modes of
variations and the temporal dynamics among curves. We demonstrate that the
proposed clustering technique outperforms other existing methods through a
Monte Carlo simulation and could handle complicated cases with slow decaying
eigenvalues. In empirical data analysis, we find that the clustering results of
age-specific mortality rates can be explained by the combination of geographic
region, ethnic groups, and socioeconomic status. We further show that our model
produces more accurate forecasts than several benchmark methods in forecasting
age-specific mortality rates.
