Detection and Mode-Identification of Multiple Change Points in Tensor Factor Models
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| Format: | Preprint |
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2026
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| _version_ | 1866917403023114240 |
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| author | Zhang, Yuqi Cen, Zetai Cho, Haeran |
| author_facet | Zhang, Yuqi Cen, Zetai Cho, Haeran |
| contents | We study the problems arising from modeling high-dimensional tensor-valued time series under a Tucker decomposition-based factor model with multiple structural change points. First, we propose an algorithm for detecting the multiple change points, which utilizes the low-rank structure of the data for statistical and computational efficiency. Also, the multi-dimensional array setting poses unique challenges, as some changes are associated with a subset of the modes, and the changes in different modes may interact with one another. Recognizing these, we investigate the problem of identifying each change with the tensor modes post-segmentation. To this end, we formalize the mode-identifiability of each change and propose an algorithm for detecting the modes at which the data are undergoing a mode-identifiable shift. We establish the consistency of both change point detection and mode-identification methods under a weak moment condition, and demonstrate their good performance on simulated datasets where, in particular, it is shown that the mode-identification step can improve the post-segmentation estimation of the mode-wise loading space. Additionally we analyze the datasets on New York City taxi usage and Fama--French portfolio returns using the proposed suite of methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_11300 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Detection and Mode-Identification of Multiple Change Points in Tensor Factor Models Zhang, Yuqi Cen, Zetai Cho, Haeran Statistics Theory Methodology We study the problems arising from modeling high-dimensional tensor-valued time series under a Tucker decomposition-based factor model with multiple structural change points. First, we propose an algorithm for detecting the multiple change points, which utilizes the low-rank structure of the data for statistical and computational efficiency. Also, the multi-dimensional array setting poses unique challenges, as some changes are associated with a subset of the modes, and the changes in different modes may interact with one another. Recognizing these, we investigate the problem of identifying each change with the tensor modes post-segmentation. To this end, we formalize the mode-identifiability of each change and propose an algorithm for detecting the modes at which the data are undergoing a mode-identifiable shift. We establish the consistency of both change point detection and mode-identification methods under a weak moment condition, and demonstrate their good performance on simulated datasets where, in particular, it is shown that the mode-identification step can improve the post-segmentation estimation of the mode-wise loading space. Additionally we analyze the datasets on New York City taxi usage and Fama--French portfolio returns using the proposed suite of methods. |
| title | Detection and Mode-Identification of Multiple Change Points in Tensor Factor Models |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2604.11300 |