  This study introduces an innovative methodology for mortality forecasting,
which integrates signature-based methods within the functional data framework
of the Hyndman-Ullah (HU) model. This new approach, termed the Hyndman-Ullah
with truncated signatures (HUts) model, aims to enhance the accuracy and
robustness of mortality predictions. By utilizing signature regression, the
HUts model aims to capture complex, nonlinear dependencies in mortality data
which enhances forecasting accuracy across various demographic conditions. The
model is applied to mortality data from 12 countries, comparing its forecasting
performance against classical models like the Lee-Carter model and variants of
the HU models across multiple forecast horizons. Our findings indicate that
overall the HUts model not only provides more precise point forecasts but also
shows robustness against data irregularities, such as those observed in
countries with historical outliers. The integration of signature-based methods
enables the HUts model to capture complex patterns in mortality data, making it
a powerful tool for actuaries and demographers. Prediction intervals are also
constructed using bootstrapping methods.
