Abstract

This paper investigates the estimation of a functional factor model characterized by factor loadings that may change over time with the number of changes

being unknown. We propose a novel procedure to detect potential breaks and

identify their locations. In the first step, we compute factor loadings for each

time point and analyze their differences between consecutive time points. In the

second step, we employ the wild binary segmentation method (WBS) to estimate both the number and positions of change points in the sequence of these

differences. In the third step, we utilize the estimated change point positions

to re-estimate the functional factor model. This results in functional data where

Huacheng Su,

School of Statistics and Data Sci-

Caixia Xu: ORCID: 0009-0005-5063-0507

Xu Liu: ORCID: 0000-0003-3829-1715

change points are known, leading to reduced fitting errors. It is crucial to emphasize that throughout the process of estimating the loading and number of factors,

we have effectively leveraged the unique characteristics of complex functional data

and mitigated the impact of unknown change points. We demonstrate that the

proposed method can correctly identify the number of changes and accurately

estimate their locations with probability approaching one.

Simulation studies

and empirical applications illustrate the excellent finite-sample performance of

our proposed approach.

Information

Preprint No.SS-2025-0014
Manuscript IDSS-2025-0014
Complete AuthorsCaixia Xu, Huacheng Su, Xu Liu, Jinhong You
Corresponding AuthorsHuacheng Su
Emailssuhuacheng79@163.com

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Acknowledgments

The authors would like to thank the Editor, the Associate Editor and two

anonymous referees for their constructive suggestions that substantially improved this paper. This work was supported by the 111-Center Project

of China (B25066), the Innovative Research Team of SUFE, the NSFC

(12271329, 72331005), the Shanghai Research Center for Data Science and

Decision Technology, the Fundamental Research Funds for the Central Universities (CXJJ-2024-455), Humanities and Social Sciences Fund of Ministry

of Education 23YJA910003.

Supplementary Materials

The online Supplementary Material contains the numerical studies, additional results of the application, lemmas and technical proofs.

Supplementary materials are available for download.