High-dimensional functional time series forecasting: An application to age-specific mortality rates

TL;DR

This paper introduces a novel two-step dimension reduction method combining dynamic functional principal component analysis and factor models to improve forecasting of high-dimensional functional time series, demonstrated on mortality data.

Contribution

A new method that effectively reduces dimensionality and forecasts high-dimensional functional time series using a combination of PCA and factor models.

Findings

Method outperforms existing approaches in simulations.

Accurately forecasts Japanese age-specific mortality rates.

Establishes asymptotic properties of the estimators.

Abstract

We address the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure. The difficulty of forecasting high-dimensional functional time series lies in the curse of dimensionality. In this paper, we propose a novel method to solve this problem. Dynamic functional principal component analysis is first applied to reduce each functional time series to a vector. We then use the factor model as a further dimension reduction technique so that only a small number of latent factors are preserved. Classic time series models can be used to forecast the factors and conditional forecasts of the functions can be constructed. Asymptotic properties of the approximated functions are established, including both estimation error and forecast error. The proposed method is easy to implement especially when the dimension of the functional time series is large. We show the superiority of our approach by both simulation studies and an application to Japanese age-specific mortality rates.