Yuefeng Han, Rong Chen, Cun-Hui Zhang, Qiwei Yao
arXiv 17 Mar 2021 · Statistics — Methodology · publishedJournal of the American Statistical Association (2022) · 8 citations (OpenAlex)
arXiv:2103.09411 · PDF · DOI · OpenAlex · Extracted main text
We propose a contemporaneous bilinear transformation for a $p\times q$ matrix time series to alleviate the difficulties in modeling and forecasting matrix time series when $p$ and/or $q$ are large. The resulting transformed matrix assumes a block structure consisting of several small matrices, and those small matrix series are uncorrelated across all times. Hence an overall parsimonious model is achieved by modelling each of those small matrix series separately without the loss of information on the linear dynamics. Such a parsimonious model often has better forecasting performance, even when the underlying true dynamics deviates from the assumed uncorrelated block structure after transformation. The uniform convergence rates of the estimated transformation are derived, which vindicate an important virtue of the proposed bilinear transformation, i.e. it is technically equivalent to the decorrelation of a vector time series of dimension max$(p,q)$ instead of $p\times q$. The proposed method is illustrated numerically via both simulated and real data examples.
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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 | Chang, J., Guo, B., and Yao, Q (2018) Principal component analysis for second-order stationary vector time series self | 1.000 | 11 | 4 | 100% |
| 2 | Chen, R., Xiao, H., and Yang, D (2021) Autoregressive models for matrix-valued time series self | 0.928 | 4 | 3 | 100% |
| 3 | Rio, E (2000) Théorie asymptotique des processus aléatoires faiblement dépendants, volume 31 of Mathématiques & Applications (Berlin) [Mathema… | 0.737 | 3 | 3 | 67% |
| 4 | Chen, R., Yang, D., and Zhang, C.-H (2022) Factor models for high-dimensional tensor time series self | 0.737 | 3 | 2 | 100% |
| 5 | Wang, D., Liu, X., and Chen, R (2019) Factor models for matrix-valued high-dimensional time series self | 0.737 | 3 | 2 | 100% |
| 6 | Hoff, P. D (2015) Multilinear tensor regression for longitudinal relational data | 0.644 | 2 | 2 | 100% |
| 7 | Chen, E. Y., Tsay, R. S., and Chen, R (2020) Constrained factor models for high-dimensional matrix-variate time series self | 0.644 | 2 | 2 | 100% |
| 8 | Han, Y., Chen, R., and Zhang, C.-H (2022) Rank determination in tensor factor model self | 0.644 | 2 | 2 | 100% |
| 9 | Lam, C. and Yao, Q (2012) Factor modeling for high-dimensional time series: inference for the number of factors self | 0.644 | 2 | 2 | 100% |
| 10 | Merlevède, F., Peligrad, M., and Rio, E (2011) A bernstein type inequality and moderate deviations for weakly dependent sequences | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 51 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | High-Dimensional Matrix-Variate Diffusion Index Models for Time Series Forecasting | 0.405 | 1 | 1 |
| 2 | Factor Models of Matrix-Valued Time Series: Nonstationarity and Cointegration | 0.405 | 1 | 1 |