Yuefeng Han, Dan Yang, Cun-Hui Zhang, Rong Chen
arXiv 29 Oct 2021 · Statistics — Methodology · publishedJournal of the Royal Statistical Society Series B (Statistical Methodology) (2024) · 17 citations (OpenAlex)
arXiv:2110.15517 · PDF · DOI · OpenAlex · Extracted main text
Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CP decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chen, R., Yang, D., and Zhang, C.-H (2022) Factor models for high-dimensional tensor time series self | 1.000 | 9 | 4 | 100% |
| 2 | Anandkumar, A., Ge, R., and Janzamin, M (2014) Guaranteed non-orthogonal tensor decomposition via alternating rank-1 updates | 1.000 | 8 | 4 | 100% |
| 3 | Lam, C. and Yao, Q (2012) Factor modeling for high-dimensional time series: inference for the number of factors | 1.000 | 5 | 4 | 100% |
| 4 | Lam, C., Yao, Q., and Bathia, N (2011) Estimation of latent factors for high-dimensional time series | 1.000 | 5 | 3 | 100% |
| 5 | Han, Y., Chen, R., Yang, D., and Zhang, C.-H (2020) Tensor factor model estimation by iterative projection self | 0.977 | 15 | 6 | 93% |
| 6 | Hao, B., Zhang, A., and Cheng, G (2020) Sparse and low-rank tensor estimation via cubic sketchings | 0.928 | 4 | 4 | 100% |
| 7 | Bai, J. and Ng, S (2002) Determining the number of factors in approximate factor models | 0.843 | 3 | 3 | 100% |
| 8 | Han, Y., Chen, R., and Zhang, C.-H (2022) Rank determination in tensor factor model self | 0.843 | 3 | 3 | 100% |
| 9 | Sun, W. W., Lu, J., Liu, H., and Cheng, G (2017) Provable sparse tensor decomposition | 0.843 | 3 | 3 | 100% |
| 10 | Chen, E. Y. and Fan, J (2023) Statistical inference for high-dimensional matrix-variate factor models | 0.737 | 3 | 2 | 100% |
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