High-dimensional functional time series forecasting

An application to age-specific mortality rates

Yuan Gao*, Han Lin Shang, Yanrong Yang

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)232-243
Number of pages12
JournalJournal of Multivariate Analysis
Volume170
DOIs
Publication statusPublished - Mar 2019
Externally publishedYes

Keywords

  • Demographic forecasting
  • Dynamic functional principal component analysis
  • Factor model
  • High-dimensional functional time series
  • Long-run covariance operator

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