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

TL;DR

This paper introduces a dual-factor model for high-dimensional functional time series that captures cross-sectional heterogeneity and temporal dynamics, improving forecasting accuracy for complex data like mortality rates.

Contribution

The paper presents a novel dual-factor modeling approach for high-dimensional functional time series, effectively capturing heterogeneity and dynamics in a unified framework.

Findings

Enhanced accuracy in mortality rate forecasting.

Effective recovery of basis functions and common features.

Improved life annuity pricing based on forecasts.

Abstract

We propose a dual-factor model for high-dimensional functional time series (HDFTS) that considers multiple populations. The HDFTS is first decomposed into a collection of functional time series (FTS) in a lower dimension and a group of population-specific basis functions. The system of basis functions describes cross-sectional heterogeneity, while the reduced-dimension FTS retains most of the information common to multiple populations. The low-dimensional FTS is further decomposed into a product of common functional loadings and a matrix-valued time series that contains the most temporal dynamics embedded in the original HDFTS. The proposed general-form dual-factor structure is connected to several commonly used functional factor models. We demonstrate the finite-sample performances of the proposed method in recovering cross-sectional basis functions and extracting common features using simulated HDFTS. An empirical study shows that the proposed model produces more accurate point and interval forecasts for subnational age-specific mortality rates in Japan. The financial benefits associated with the improved mortality forecasts are translated into a life annuity pricing scheme.