Jinyuan Chang, Yue Du, Guanglin Huang, Qiwei Yao
arXiv 8 Oct 2024 · Statistics — Methodology · publishedThe Annals of Statistics (2026)
arXiv:2410.05634 · PDF · DOI · OpenAlex · Extracted main text
We propose a new method for identifying and estimating the CP-factor models for matrix time series. Unlike the generalized eigenanalysis-based method of Chang et al. (2023) for which the convergence rates of the associated estimators may suffer from small eigengaps as the asymptotic theory is based on some matrix perturbation analysis, the proposed new method enjoys faster convergence rates which are free from any eigengaps. It achieves this by turning the problem into a joint diagonalization of several matrices whose elements are determined by a basis of a linear system, and by choosing the basis carefully to avoid near co-linearity (see Proposition 5 and Section 4.3). Furthermore, unlike Chang et al. (2023) which requires the two factor loading matrices to be full-ranked, the proposed new method can handle rank-deficient factor loading matrices. Illustration with both simulated and real matrix time series data shows the advantages of the proposed new method.
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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 | Han, Y., Yang, D., Zhang, C., and Chen, R (2024) CP factor model for dynamic tensors | 1.000 | 17 | 4 | 100% |
| 2 | Chang, J., Guo, B., and Yao, Q (2015) High dimensional stochastic regression with latent factors, endogeneity and nonlinearity self | 1.000 | 8 | 5 | 100% |
| 3 | Lam, C. and Yao, Q (2012) Factor modeling for high-dimensional time series: inference for the number of factors self | 1.000 | 7 | 4 | 100% |
| 4 | Chang, J., He, J., Yang, L., and Yao, Q (2023) Modelling matrix time series via a tensor CP-decomposition self | 0.956 | 40 | 10 | 88% |
| 5 | Chang, J., Guo, B., and Yao, Q (2018) Principal component analysis for second-order stationary vector time series self | 0.737 | 4 | 4 | 50% |
| 6 | Lam, C., Yao, Q., and Bathia, N (2011) Estimation of latent factors for high-dimensional time series self | 0.737 | 3 | 2 | 100% |
| 7 | Wang, D., Liu, X., and Chen, R (2019) Factor models for matrix-valued high-dimensional time series | 0.737 | 3 | 2 | 100% |
| 8 | Han, Y., Chen, R., Yang, D., and Zhang, C.-H (2024) Tensor factor model estimation by iterative projection | 0.644 | 2 | 2 | 100% |
| 9 | Kolda, T. G. and Bader, B. W (2009) Tensor decompositions and applications | 0.644 | 2 | 2 | 100% |
| 10 | Ziehe, A., Laskov, P., Nolte, G., and Müller, K. R (2004) A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 26 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Modewise Additive Factor Model for Matrix Time Series | 0.644 | 2 | 2 |
| 2 | CP-Factorization for High Dimensional Tensor Time Series and Double Projection Iterations | 0.585 | 3 | 1 |