  In areas of application, including actuarial science and demography, it is
increasingly common to consider a time series of curves; an example of this is
age-specific mortality rates observed over a period of years. Given that age
can be treated as a discrete or continuous variable, a dimension reduction
technique, such as principal component analysis, is often implemented. However,
in the presence of moderate to strong temporal dependence, static principal
component analysis commonly used for analyzing independent and identically
distributed data may not be adequate. As an alternative, we consider a
\textit{dynamic} principal component approach to model temporal dependence in a
time series of curves. Inspired by Brillinger's (1974) theory of dynamic
principal components, we introduce a dynamic principal component analysis,
which is based on eigen-decomposition of estimated long-run covariance. Through
a series of empirical applications, we demonstrate the potential improvement of
one-year-ahead point and interval forecast accuracies that the dynamic
principal component regression entails when compared with the static
counterpart.
