Abstract

Factor models have been extensively employed in high dimensional

time series. However, little is known for the case with the sparse loading matrix.

This paper introduces a sparse factor model with an easy-to-implement estimation method, aiming to enhance interpretability and relax the constraints on the

dimension p of the time series. In particular, it is shown that under weak conditions, the loading space could be consistently estimated with a convergence rate

related to the sparseness of each column in the loading matrix and the eigenvalues

used to recover the latent factor and loading matrix. In addition, a randomized

sequential test is introduced to determine the number of sparse factors. Simulations and real data analysis on sea surface air pressure and stock portfolios are

also provided to illustrate the performance of the proposed method.

Information

Preprint No.SS-2023-0219
Manuscript IDSS-2023-0219
Complete AuthorsXiaoran Wu, Baojun Dou, Rongmao Zhang
Corresponding AuthorsRongmao Zhang
Emailsrmzhang@zju.edu.cn

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Acknowledgments

We would like to thank the Co-Editor, Associate Editor and two anonymous

referees for their critical comments and thoughtful suggestions, which led to

a much improved version of this paper. This research was supported in part

by grants from NSFC, China (Nos. 12171427, U21A20426) and National

Key R&D Program of China (2024YFA1013502).

Supplementary Materials

The supplementary materials contains some technical lemmas, the proof of

Theorem 1-4 of the main article, and some detailed tables and figures of

simulation results which are discussed in the main paper.

Supplementary materials are available for download.