# Forecasting high-dimensional functional time series: Application to sub-national age-specific mortality

**Authors:** Cristian F. Jiménez-Varón, Ying Sun, Han Lin Shang  
**arXiv:** [2305.19749](https://arxiv.org/abs/2305.19749)  
**Date:** 2023-05-31  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2305.19749v1/

## Key points

- Study focuses on modeling and forecasting high-dimensional functional time series (HDFTS) with cross-sectional correlation and temporal dependence
- Introduces a novel two-way functional median polish decomposition method to decompose HDFTS into deterministic and time-varying components, enhancing robustness against outliers
- Forecasting approach utilizes dynamic functional principal component analysis to generate accurate forecast curves for multiple populations by combining forecasts with deterministic components
- Methodology applied to age- and sex-specific mortality rates from the US, France, and Japan, demonstrating effectiveness in various sub-national regions
- Outperforms benchmark methods in point and interval forecasts for multi-population mortality, but performance varies across countries due to unique characteristics and population structures
- Opportunities for further extension include addressing impact of outliers on principal component scores through robust methods, as well as integrating additional levels of disaggregation such as cause-of-death or socioeconomic status for enhanced accuracy and applicability

## Summary

, , , , 

This study focuses on modeling and forecasting high-dimensional functional time series (HDFTS) with cross-sectional correlation and temporal dependence. A novel two-way functional median polish decomposition method is introduced to effectively decompose HDFTS into deterministic and time-varying components, providing robustness against outliers. The forecasting approach utilizes dynamic functional principal component analysis to generate accurate forecast curves for multiple populations by combining these forecasts with the deterministic components. The methodology is applied to age- and sex-specific mortality rates from the US, France, and Japan, showcasing its effectiveness in various sub-national regions. It outperforms several benchmark methods in terms of point and interval forecasts for multi-population mortality. However, the forecasting performance varies across countries due to their unique characteristics and population structures. Opportunities for further extension of this methodology include addressing the impact of outliers on principal component scores through robust functional principal component analysis or other robust time series methods. Additionally, additional levels of disaggregation such as cause-of-death or socioeconomic status could be integrated into the model with appropriate data availability, enhancing its accuracy and applicability in diverse mortality data scenarios.