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This paper proposes a two-fold factor model for high-dimensional functionaltime series (HDFTS), which enables the modeling and forecasting ofmulti-population mortality under the functional data framework. The proposedmodel first decomposes the HDFTS into functional time series with lowerdimensions (common feature) and a system of basis functions specific todifferent cross-sections (heterogeneity). Then the lower-dimensional commonfunctional time series are further reduced into low-dimensional scalar factormatrices. The dimensionally reduced factor matrices can reasonably conveyuseful information in the original HDFTS. All the temporal dynamics containedin the original HDFTS are extracted to facilitate forecasting. The proposedmodel can be regarded as a general case of several existing functional factormodels. Through a Monte Carlo simulation, we demonstrate the performance of theproposed method in model fitting. In an empirical study of the Japanesesubnational age-specific mortality rates, we show that the proposed modelproduces more accurate point and interval forecasts in modelingmulti-population mortality than those existing functional factor models. Thefinancial impact of the improvements in forecasts is demonstrated throughcomparisons in life annuity pricing practices.

Multi-population mortality forecasting using high-dimensional functional factor models