Dynamic principal component regression for forecasting functional time series in a group structure

TL;DR

This paper introduces a dynamic functional principal component regression method for forecasting grouped functional time series, improving accuracy when temporal dependence is present, with applications to Japanese mortality data.

Contribution

It extends static PCA to dynamic PCA for better forecasting of grouped functional time series, ensuring coherence across hierarchical levels.

Findings

Dynamic PCA improves forecast accuracy under temporal dependence.

The method maintains coherence in group forecasts.

Application to Japanese mortality data demonstrates effectiveness.

Abstract

When generating social policies and pricing annuity at national and subnational levels, it is essential both to forecast mortality accurately and ensure that forecasts at the subnational level add up to the forecasts at the national level. This has motivated recent developments in forecasting functional time series in a group structure, where static principal component analysis is used. In the presence of moderate to strong temporal dependence, static principal component analysis designed for independent and identically distributed functional data may be inadequate. Thus, through using the dynamic functional principal component analysis, we consider a functional time series forecasting method with static and dynamic principal component regression to forecast each series in a group structure. Through using the regional age-specific mortality rates in Japan obtained from the Japanese Mortality Database (2019), we investigate the point and interval forecast accuracies of our proposed extension, and subsequently make recommendations.