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We propose a dual-factor model for high-dimensional functional time series(HDFTS) that considers multiple populations. The HDFTS is first decomposed intoa collection of functional time series (FTS) in a lower dimension and a groupof population-specific basis functions. The system of basis functions describescross-sectional heterogeneity, while the reduced-dimension FTS retains most ofthe information common to multiple populations. The low-dimensional FTS isfurther decomposed into a product of common functional loadings and amatrix-valued time series that contains the most temporal dynamics embedded inthe original HDFTS. The proposed general-form dual-factor structure isconnected to several commonly used functional factor models. We demonstrate thefinite-sample performances of the proposed method in recovering cross-sectionalbasis functions and extracting common features using simulated HDFTS. Anempirical study shows that the proposed model produces more accurate point andinterval forecasts for subnational age-specific mortality rates in Japan. Thefinancial benefits associated with the improved mortality forecasts aretranslated into a life annuity pricing scheme.

Forecasting high-dimensional functional time series with dual-factor structures