Resources of Analysis of Tensor Time Series

by Rong Chen, Shuo-Chieh Huang, and Stevenson Bolivar

This webpage presents a list of references and R packages related to Tensor Time Series. It is by no means exhaustive and obviously biased towards our work and the work of our close colleagues. We keep on adding stuff from time to time, although not as often as we should.

If we miss your work related to tensor time series, please send it to This email address is being protected from spambots. You need JavaScript enabled to view it.. Please also send your new papers so we can keep update the page.

Tensor Autoregressive Models

+ - Precursor: Matrix Autoregressive Models Click to collapse

[1] J. C. Chan and Y. Qi. “Large Bayesian matrix autoregressions”. In: Journal of Econometrics (2025), p. 105955. DOI: https://doi.org/10.1016/j.jeconom.2025.105955.

[2] R. Chen, H. Xiao, and D. Yang. “Autoregressive models for matrix-valued time series”. In: Journal of Econometrics 222.1 (2021), pp. 539–560. DOI: https://doi.org/10.1016/j.jeconom.2020.07.015

[3] R. S. Tsay. “Matrix-Variate Time Series Analysis: A Brief Review and Some New Developments”. In: International Statistical Review 92.2 (2024), pp. 246–262. DOI: https://doi.org/10.1111/insr.12558.

[4] D. Wang, X. Liu, and R. Chen. “Factor models for matrix-valued high-dimensional time series”. In: Journal of Econometrics 208.1 (2019), pp. 231–248. DOI: https://doi.org/10.1016/j.jeconom.2018.09.013. URL: https://arxiv.org/abs/1610.01889.

[5] H. Xiao, Y. Han, R. Chen, et al. Reduced Rank Autoregressive Models for Matrix Time Series. Tech. rep. Technical Report. Rutgers University, 2021. URL: https://statweb.rutgers.edu/hxiao/rrmar.pdf.

[6] S. Y. Samadi, and T. P. De Alwis. “Envelope Matrix Autoregressive Models”. In: Journal of Business & Economic Statistics (2025), pp. 1–16. DOI: https://doi.org/10.1080/07350015.2025.2537404

+ - Tensor autoregressive models Click to collapse

[1] Z. Li and H. Xiao. Multi-linear Tensor Autoregressive Models. 2021. arXiv: 2110.00928 [stat.ME]. URL: https://arxiv.org/abs/2110.00928.

[2] D. Wang, Y. Zheng, and G. Li. “High-dimensional low-rank tensor autoregressive time series modeling”. In: Journal of Econometrics 238.1 (2024), p. 105544. DOI: https://doi.org/10.1016/j.jeconom.2023.105544.

[3] Y. Cai, L. Li, Y. Wang, and G. Li. An efficient and Interpretable Autoregressive Model for High-Dimensional Tensor-Valued Time Series. 2025. arXiv: 2506.01658 [stat.ME]. URL: https://arxiv.org/abs/2506.01658

+ - Extensions of TenAR models and other related models Click to collapse

[1] N. Hsu, H. Huang, and R. S. Tsay. “Matrix Autoregressive Spatio-Temporal Models”. In: Journal of Computational and Graphical Statistics 30.4 (2021), pp. 1143–1155. DOI: https://doi.org/10.1080/10618600.2021.1938587.

[2] Z. Li and H. Xiao. “Cointegrated Matrix Autoregression Models”. In: arXiv:2409.10860 stat.ME. URL: https://arxiv.org/abs/2409.10860.

[3] C. Yu, D. Li, F. Jiang, et al. “Matrix GARCH Model: Inference and Application”. In: Journal of the American Statistical Association 0.0 (2024), pp. 1–31. DOI: https://doi.org/10.1080/01621459.2024.2415719.

[4] C. Yu, D. Li, X. Zhang, et al. “Two-way Matrix Autoregressive Model with Thresholds”. In: arXiv:2407.10272stat.ME. arXiv: 2407.10272 [stat.ME]. URL: https://arxiv.org/abs/2407.10272.

Matrix and Tensor Factor Model

+ - Tensor Factor Model in Tucker form Click to collapse

[1] M. Banin, M. Barigozzi, L. Trapin. Predicting Energy Demand with Tensor Factor Models. 2025. arXiv: 2502.06213 [stat.AP] URL: https://arxiv.org/abs/2502.06213

[2] M. Barigozzi, H. Cho, and H. Maeng. Tail-robust factor modelling of vector and tensor time series in high dimensions. 2025. arXiv: 2407.09390 [stat.ME]. URL: https://arxiv.org/abs/2407.09390.

[3] M. Barigozzi, Y. He, L. Li, et al. Robust Tensor Factor Analysis. 2023. arXiv: 2303.18163 [stat.ME]. URL: https://arxiv.org/abs/2303.18163.

[4] M. Barigozzi, Y. He, L. Li, et al. “Statistical inference for large-dimensional tensor factor model by iterative projections”. In: arXiv preprint (2023). URL: https://arxiv.org/abs/2206.09800.

[5] E. Y. Chen and J. Fan. “Statistical inference for high-dimensional matrix-variate factor models”. In: Journal of the American Statistical Association 0.0 (2021), pp. 1-18. DOI: https://www.tandfonline.com/doi/full/10.1080/01621459.2021.1970569. URL: https://arxiv.org/abs/2001.01890.

[6] R. Chen, D. Yang, and C. Zhang. “Factor models for high-dimensional tensor time series”. In: Journal of the American Statistical Association (2022), pp. 1–23. DOI: https://doi.org/10.1080/01621459.2021.1912757. URL: https://arxiv.org/abs/1905.07530.

[7] W. Chen and C. Lam. “Rank and factor loadings estimation in time series tensor factor model by pre-averaging”. In: The Annals of Statistics 52.1 (2024), pp. 364 – 391. DOI: https://doi.org/10.1214/23-AOS2350.

[8] Y. Han, R. Chen, D. Yang, et al. “Tensor Factor Model Estimation by Iterative Projection”. In: The Annals of Statistics 52 (2024), pp. 2641–2667. DOI: "https://doi.org/10.1214/24-AOS2412. URL: https://arxiv.org/abs/2006.02611.

[9] Y. Han, R. Chen, and C. Zhang. “Rank determination in tensor factor model”. In: Electronic Journal of Statistics 16.1 (2022), pp. 1726–1803. DOI: https://doi.org/10.1214/22-EJS1991. URL: https://arxiv.org/abs/2011.07131.

[10] Y. He, X. Kong, D. Liu, et al. Robust Statistical Inference for Large-dimensional Matrix-valued Time Series via Iterative Huber Regression. 2023. arXiv: 2306.03317 [stat.ME]. URL: https://arxiv.org/abs/2306.03317.

[11] Y. He, X. Kong, L. Yu, et al. “Matrix Factor Analysis: From Least Squares to Iterative Projection”. In: Journal of Business & Economic Statistics 0.0 (2023), pp. 1-13. DOI: https://doi.org/10.1080/07350015.2023.2191676. URL: https://arxiv.org/abs/2112.04186.

[12] D. Wang, X. Liu, and R. Chen. “Factor models for matrix-valued high-dimensional time series”. In: Journal of Econometrics 208.1 (2019), pp. 231–248. DOI: https://doi.org/10.1016/j.jeconom.2018.09.013. URL: https://arxiv.org/abs/1610.01889.

[13] Y. Wang, Y. Zhu, Q. Sun, et al. “Adaptively robust high-dimensional matrix factor analysis under Huber loss function”. In: Journal of Statistical Planning and Inference 231 (2024), p. 106137. ISSN: 0378-3758. DOI: https://doi.org/10.1016/j.jspi.2023.106137. URL: https://www.sciencedirect.com/science/article/pii/S0378375823001064.

[14] L. Yu, Y. He, X. Kong, et al. “Projected estimation for large-dimensional matrix factor models”. In: Journal of Econometrics 229.1 (2022), pp. 201-217. ISSN: 0304-4076. DOI: https://doi.org/10.1016/j.jeconom.2021.04.001. URL: https://www.sciencedirect.com/science/article/pii/S0304407621001123.

[15] W. Zhang. Bayesian Dynamic Factor Models for High-dimensional Matrix-valued Time Series. 2024. arXiv: 2409.08354 [econ.EM]. URL: https://arxiv.org/abs/2409.08354.

[16] X. Zhang, G. Li, C. C. Liu, et al. Tucker tensor factor models: matricization and mode-wise PCA estimation. 2024. arXiv: 2206.02508 [stat.ME]. URL: https://arxiv.org/abs/2206.02508.

+ - Tensor Factor Models in CP form Click to collapse

[1] J. Chang, Y. Du, G. Huang, et al. Identification and estimation for matrix time series CP-factor models. 2025. arXiv: 2410.05634 [stat.ME]. URL: https://arxiv.org/abs/2410.05634.

[2] J. Chang, J. He, L. Yang, et al. “Modelling matrix time series via a tensor CP-decomposition”. In: Journal of the Royal Statistical Society Series B: Statistical Methodology 85.1 (Jan. 2023), pp. 127–148. DOI: https://academic.oup.com/jrsssb/article/85/1/127/7008470.

[3] B. Chen, Y. Han, and Q. Yu. “Estimation and Inference for CP Tensor Factor Models”. In: arXiv:2406.17278 stat.ME. URL: https://arxiv.org/abs/2406.17278.

[4] Y. Han, D. Yang, C. Zhang, et al. “CP factor model for dynamic tensors”. In: Journal of the Royal Statistical Society Series B: Statistical Methodology (2024), p. qkae036. DOI: https://doi.org/10.1093/jrsssb/qkae036. URL: https://arxiv.org/abs/2110.15517.

+ - Extension of TFM and other related models Click to collapse

[1] A. Babii, E. Ghysels, and J. Pan. Tensor PCA for Factor Models. 2025. arXiv: 2212.12981 [econ.EM]. URL: https://arxiv.org/abs/2212.12981.

[2] A. Babii, E. Ghysels, and J. Pan. Tensor Principal Component Analysis. 2023. arXiv: 2212.12981 [econ.EM]. URL: https://arxiv.org/abs/2212.12981.

[3] M. Barigozzi, D. L. Vecchia, and H. Liu. “General spatio-temporal factor models for high-dimensional random fields on a lattice”. In: The Annals of Statistics 53.1 (2025), pp. 268 – 294. DOI: https://doi.org/10.1214/24-AOS2466. URL: https://doi.org/10.1214/24-AOS2466.

[4] S. Bolivar, Y. Han and R. Chen. Threshold Tensor Factor Model in CP Form. 2025. arXiv: 2511.19796 [stat.ME]. URL: http://arxiv.org/abs/2511.19796.

[5] Z. Cen and C. Lam. “On Testing Kronecker Product Structure in Tensor Factor Models”. In: arXiv preprint (2025). URL: https://arxiv.org/abs/2501.11208.

[6] B. Chen, E. Y. Chen, S. Bolivar, and R. Chen. Time-Varying Matrix Factor Models. 2024. URL: https://arxiv.org/abs/2404.01546.

[7] B. Chen, Y. Han, Q. Yu. “Diffusion index forecasting with tensor data”. In: Journal of Econometrics 254 (2026): 106204. DOI: https://doi.org/10.1016/j.jeconom.2026.106204. URL: https://arxiv.org/abs/2511.02235.

[8] E. Y. Chen, J. Fan, and X. Zhu. “Factor Augmented Matrix Regression”. In: Journal of the American Statistical Association 100(2025), pp. 1-14. DOI: https://doi.org/10.1080/01621459.2025.2595734. URL: https://arxiv.org/abs/2405.17744.

[9] E. Y. Chen, R. S. Tsay, and R. Chen. “Constrained Factor Models for High-Dimensional Matrix-Variate Time Series”. In: Journal of the American Statistical Association 115.530 (2020), pp. 775-793. DOI: https://www.tandfonline.com/doi/full/10.1080/01621459.2019.1584899. URL: https://arxiv.org/abs/1710.06075.

[10] E. Y. Chen, D. Xia, C. Cai, et al. “Semi-parametric tensor factor analysis by iteratively projected singular value decomposition”. In: Journal of the Royal Statistical Society Series B: Statistical Methodology 86.3 (Feb. 2024), pp. 793–823. DOI: https://doi.org/10.1093/jrsssb/qkae001. URL: https://doi.org/10.1093/jrsssb/qkae001.

[11] E. Y. Chen, Y. Han, J. Li, and K. Xu. “Modewise Additive Factor Model for Matrix Time Series”. 2026. URL: https://arxiv.org/pdf/2512.25025.

[12] R. Chen, S. Giannerini, G. Goracci, et al. Inference in matrix-valued time series with common stochastic trends and multifactor error structure. 2025. arXiv: 2501.01925 [stat.ME]. URL: https://arxiv.org/abs/2501.01925.

[13] W. Chen and C. Lam. Factor Strength Estimation in Vector and Matrix Time Series Factor Models. 2024. arXiv: 2405.07294 [stat.ME]. URL: https://arxiv.org/abs/2405.07294.

[14] W. Chen and C. Lam. “Estimation of Coupled Vector-Tensor Group Factor Model”. 2026. URL: https://doi.org/10.2139/ssrn.5984015

[15] B. K. Fosdick and P. D. Hoff. “Separable factor analysis with applications to mortality data”. In: The Annals of Applied Statistics 8.1 (2014), pp. 120 – 147. DOI: https://doi.org/10.1214/13-AOAS694. URL: https://doi.org/10.1214/13-AOAS694.

[16] Z. Gao and R. S. Tsay. “A Two-Way Transformed Factor Model for Matrix-Variate Time Series”. In: Econometrics and Statistics 27 (2023), pp. 83–101. DOI: https://doi.org/10.1016/j.ecosta.2021.08.008.

[17] Y. He, X. Kong, L. Trapani, et al. “Online change-point detection for matrix-valued time series with latent two-way factor structure”. In: The Annals of Statistics 52.4 (2024), pp. 1646–1670. DOI: https://doi.org/10.1214/24-AOS2410. URL: https://doi.org/10.1214/24-AOS2410.

[18] P. D. Hoff. “Multilinear tensor regression for longitudinal relational data”. In: The Annals of Applied Statistics 9.3 (2015), pp. 1169 – 1193. DOI: https://doi.org/10.1214/15-AOAS839. URL: https://doi.org/10.1214/15-AOAS839.

[19] C. E. Lee and X. Zhang. “Conditional mean dimension reduction for tensor time series”. In: Computational Statistics & Data Analysis 199 (2024), p. 107998. DOI: https://doi.org/10.1016/j.csda.2024.107998.

[20] O. B. Linton and H. Tang. “Comment on “Factor Models for High-Dimensional Tensor Time Series” by Rong Chen, Dan Yang, and Cun-Hui Zhang”. In: Journal of the American Statistical Association 117.537 (2022), pp. 117–117. DOI: https://doi.org/10.1080/01621459.2021.2018328. eprint: https://doi.org/10.1080/01621459.2021.2018328. URL: https://doi.org/10.1080/01621459.2021.2018328.

[21] O. B. Linton and H. Tang. “ESTIMATION OF THE Kronecker COVARIANCE MODEL BY QUADRATIC FORM”. In: Econometric Theory 38.5 (2022), p. 1014–1067. DOI: https://doi.org/10.1017/S026646662000050X.

[22] X. Liu and E. Y. Chen. “Identification and estimation of threshold matrix-variate factor models”. In: Scandinavian Journal of Statistics 49.3 (2022), pp. 1383–1417. DOI: https://doi.org/10.1111/sjos.12576. eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/sjos.12576. URL: https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12576.

[23] D. Wang, Y. Zheng, H. Lian, et al. High-dimensional vector autoregressive time series modeling via tensor decomposition. 2020. arXiv: 1909.06624 [stat.ME]. URL: https://arxiv.org/abs/1909.06624.

Other Approaches

+ - Dynamic tensor factor models Click to collapse

[1] M. Barigozzi and L. Trapin. Estimation of large approximate dynamic matrix factor models based on the EM algorithm and Kalman filtering. 2025. arXiv: 2502.04112 [stat.ME]. URL: https://arxiv.org/abs/2502.04112.

[2] R. Yu, R. Chen, H. Xiao, et al. Dynamic Matrix Factor Models for High Dimensional Time Series. 2024. arXiv: 2407.05624 [stat.ME]. URL: https://arxiv.org/abs/2407.05624.

[3] C. Yuan, Z. Gao, X. He, et al. “Two-way dynamic factor models for high-dimensional matrix-valued time series”. In: Journal of the Royal Statistical Society Series B: Statistical Methodology 85.5 (Aug. 2023), pp. 1517-1537. ISSN: 1369-7412. DOI: https://doi.org/10.1093/jrsssb/qkad077. eprint: https://academic.oup.com/jrsssb/article-pdf/85/5/1517/56555317/qkad077.pdf. URL: https://doi.org/10.1093/jrsssb/qkad077.

+ - Segmentation approaches Click to collapse

[1] Y. Han, R. Chen, C. Zhang, et al. “Simultaneous Decorrelation of Matrix Time Series”. In: Journal of the American Statistical Association 119.546 (2024), pp. 957–969. DOI: 10.1080/01621459.2022.2151448.

Software

+ - R packages Click to collapse

[1] M. Barigozzi, Y. He, L. Trapani, et al. RTFA: Robust Factor Analysis for Tensor Time Series. R package version 0.1.0. 2023. URL: https://CRAN.R-project.org/package=RTFA.

[2] Z. Cen. tensorMiss: Handle Missing Tensor Data with C++ Integration. R package version 1.1.1. 2024. URL: https://CRAN.R-project.org/package=tensorMiss.

[3] J. Chang, J. He, C. Lin, et al. HDTSA: An R package for high-dimensional time series analysis. 2024. arXiv: 2412.17341 [stat.CO]. URL: https://arxiv.org/abs/2412.17341.

[4] J. Chang, J. He, C. Lin, et al. HDTSA: High Dimensional Time Series Analysis Tools. R package version 1.0.5-1. 2025. URL: https://CRAN.R-project.org/package=HDTSA.

[5] W. Chen. TensorPreAve: Rank and Factor Loadings Estimation in Time Series Tensor Factor Models. R package version 1.1.0. 2023. URL: https://CRAN.R-project.org/package=TensorPreAve.

[6] Y. He, L. Li, D. Liu, et al. HDRFA: High-Dimensional Robust Factor Analysis. R package version 0.1.5. 2024. URL: https://CRAN.R-project.org/package=HDRFA.

[7] Z. Li, R. Yu, R. Chen, et al. tensorTS: Factor and Autoregressive Models for Tensor Time Series. R package version 1.0.2. 2024. URL: https://CRAN.R-project.org/package=tensorTS.