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In arenas of application, including demography, it is increasingly common to consider a time series of curves observed at a set of dense grid points. An example of this is age-speciﬁc mortality observed over a period of years. Since age can be viewed as an inﬁnite-dimensional continuum, a dimension reduction technique such as functional principal component analysis is often implemented. However, in the presence of temporal dependence, static functional principal component analysis commonly used for analyzing independent and identically distributed functional data may not be adequate. Instead, we consider a dynamic functional principal component analysis, which is based on eigen-decomposition of long-run covariance function, to model temporal dependence in a time series of curves. From the dynamic functional principal components and their scores, we apply functional time series forecasting methods to forecast each series in a group structure. The methodology is illustrated by age-speciﬁc Japanese mortality rates from 1975 to 2015
Cass Business School, 106 Bunhill Row
106 Bunhill Row, London EC1Y 8TZ, UK
Australian National University, College of Business and Economics
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