December 2022 Clustering and forecasting multiple functional time series
Chen Tang, Han Lin Shang, Yanrong Yang
Author Affiliations +
Ann. Appl. Stat. 16(4): 2523-2553 (December 2022). DOI: 10.1214/22-AOAS1602


Modeling and forecasting homogeneous age-specific mortality rates of multiple countries could lead to improvements in long-term forecasting. Data fed into joint models are often grouped according to nominal attributes, such as geographic regions, ethnic groups, and socioeconomic status, which may still contain heterogeneity and deteriorate the forecast results. Our paper proposes a novel clustering technique to pursue homogeneity among multiple functional time series, based on functional panel data modeling, to address this issue. Using a functional panel data model with fixed effects, we can extract common functional time series features. These common features could be decomposed into two components: the functional time trend and the mode of variations of functions (functional pattern). The functional time trend reflects the dynamics across time, while the functional pattern captures the fluctuations within curves. The proposed clustering method searches for homogeneous age-specific mortality rates of multiple countries by accounting for both the modes of variations and the temporal dynamics among curves. We demonstrate that the proposed clustering technique outperforms other existing methods through a Monte Carlo simulation and could handle complicated cases with slow decaying eigenvalues. In empirical data analysis we find that the clustering results of age-specific mortality rates can be explained by the combination of geographic region, ethnic groups, and socioeconomic status. We further show that our model produces more accurate forecasts than several benchmark methods in forecasting age-specific mortality rates.

Funding Statement

The first author would like to acknowledge the financial support of a Ph.D. scholarship from the Australian National University.


The authors would like to thank the Editor, Professor Jeffrey S. Morris, the Associate Editor, and reviewers for their insightful comments and suggestions which led to a much-improved manuscript. The authors are grateful for the insightful discussions with the 12th International Conference of the ERCIM WG participants on Computational and Methodological Statistics 2019.


Download Citation

Chen Tang. Han Lin Shang. Yanrong Yang. "Clustering and forecasting multiple functional time series." Ann. Appl. Stat. 16 (4) 2523 - 2553, December 2022.


Received: 1 June 2020; Revised: 1 January 2022; Published: December 2022
First available in Project Euclid: 26 September 2022

MathSciNet: MR4489222
zbMATH: 1498.62327
Digital Object Identifier: 10.1214/22-AOAS1602

Keywords: age-specific mortality forecasting , Functional panel data , functional principal component analysis , functional time series , multilevel functional data

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.16 • No. 4 • December 2022
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