# Factor Models for High-Dimensional Tensor Time Series

arXiv: https://arxiv.org/abs/1905.07530 · HTML: https://mlsanity.com/paper/1905.07530/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2019.

## Built on by (most cited first, 20 of 20)

- [Tensor Principal Component Analysis in High Dimensional CP Models](https://mlsanity.com/paper/2108.04428/) (2021)
- [Factor Augmented Tensor-on-Tensor Neural Networks](https://mlsanity.com/paper/2405.19610/) (2024)
- [Modelling matrix time series via a tensor CP-decomposition](https://mlsanity.com/paper/2112.15423/) (2021)
- [Covariate-assisted Sparse Tensor Completion](https://mlsanity.com/paper/2103.06428/) (2021)
- [Multi-dimensional domain generalization with low-rank structures](https://mlsanity.com/paper/2309.09555/) (2023)
- [Guaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theory](https://mlsanity.com/paper/2501.15388/) (2025)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [Econometrics of Machine Learning Methods in Economic Forecasting](https://mlsanity.com/paper/2308.10993/) (2023)
- [Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges](https://mlsanity.com/paper/2405.18412/) (2024)
- [Statistical Inference in Tensor Completion: Optimal Uncertainty Quantification and Statistical-to-Computational Gaps](https://mlsanity.com/paper/2410.11225/) (2024)
- [TEAFormers: TEnsor-Augmented Transformers for Multi-Dimensional Time Series Forecasting](https://mlsanity.com/paper/2410.20439/) (2024)
- [Factorized Fusion Shrinkage for Dynamic Relational Data](https://mlsanity.com/paper/2210.00091/) (2022)
- [Bivariate Matrix-valued Linear Regression (BMLR): Finite-sample performance under Identifiability and Sparsity Assumptions](https://mlsanity.com/paper/2412.17749/) (2024)
- [Sparsity-Induced Global Matrix Autoregressive Model with Auxiliary Network Data](https://mlsanity.com/paper/2503.08579/) (2025)
- [Score-Based Model for Low-Rank Tensor Recovery](https://mlsanity.com/paper/2506.22295/) (2025)
- [LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion](https://mlsanity.com/paper/2508.03755/) (2025)
- [Feature Augmentations for High-Dimensional Learning](https://mlsanity.com/paper/2509.00232/) (2025)
- [Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transform](https://mlsanity.com/paper/2512.10191/) (2025)
- [Are Whitepaper Claims Reflected in Market Structure? A Contamination-Aware Pipeline and a Power-Limited Null](https://mlsanity.com/paper/2601.20336/) (2026)
- [Bayesian Poisson-Randomized Gamma Tensor Factorization with Application to International Trade Flows](https://mlsanity.com/paper/2606.17267/) (2026)

## Abstract (arXiv)

Large tensor (multi-dimensional array) data are now routinely collected in a wide range of applications, due to modern data collection capabilities. Often such observations are taken over time, forming tensor time series. In this paper we present a factor model approach for analyzing high-dimensional dynamic tensor time series and multi-category dynamic transport networks. Two estimation procedures along with their theoretical properties and simulation results are presented. Two applications are used to illustrate the model and its interpretations.