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Grouped multivariate and functional time series forecasting: an application to annuity pricing

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Figure

Fig. 1. Functional Time Series Graphical Displays
Fig. 2. Image Plots Showing Log Ratios of Mortality Rates
Fig. 3. The Japanese Geographical Hierarchy Tree Diagram, With Eight Regions and 47 Prefectures
Fig. 4. Functional Principal Component Decomposition for the Female Mortality Data in HokkaidoNote: In the bottom panels, the solid blue line represents the point forecasts of scores, and the dark-and light-gray regions represent the 80% and 95% pointwise prediction intervals, respectively.
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