Results of the summarizing process for the arXiv paper: 2305.19749v1

, , , , 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.

• 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

Introduction: The study of mortality rates is crucial for understanding population dynamics and making informed policy decisions. However, traditional methods of modeling and forecasting mortality rates have limitations when dealing with high-dimensional data that exhibit cross-sectional correlation and temporal dependence. This research paper proposes a novel approach to address these challenges by introducing a two-way functional median polish decomposition method and utilizing dynamic functional principal component analysis for forecasting.

Methodology: The first step in the proposed methodology is to decompose the high-dimensional functional time series (HDFTS) into deterministic and time-varying components using the two-way functional median polish decomposition method. This approach effectively deals with outliers, providing robustness to the model. The deterministic components capture long-term trends, while the time-varying components account for short-term fluctuations in the data.

Next, dynamic functional principal component analysis is applied to generate accurate forecast curves for multiple populations by combining these forecasts with the deterministic components. This allows for incorporating cross-sectional correlation and temporal dependence in the forecasting process, resulting in more accurate predictions compared to traditional methods.

Application: To showcase its effectiveness, this methodology is applied to age- and sex-specific mortality rates from three countries - US, France, and Japan. These countries were chosen due to their diverse characteristics and population structures. The results demonstrate that this approach outperforms several benchmark methods in terms of point and interval forecasts for multi-population mortality.

Discussion: While this methodology shows promising results, there are opportunities for further extension. One such opportunity is addressing the impact of outliers on principal component scores through robust functional principal component analysis or other robust time series methods. Additionally, integrating additional levels of disaggregation such as cause-of-death or socioeconomic status could enhance its accuracy and applicability in diverse mortality data scenarios.

Conclusion: In conclusion, this research paper presents a novel approach for modeling and forecasting high-dimensional functional time series with cross-sectional correlation and temporal dependence. By utilizing two-way functional median polish decomposition and dynamic functional principal component analysis, this methodology provides robustness against outliers and accurately predicts mortality rates for multiple populations. Further research and application of this approach could greatly benefit the field of mortality forecasting.