# Modelling matrix time series via a tensor CP-decomposition

arXiv: https://arxiv.org/abs/2112.15423 · HTML: https://mlsanity.com/paper/2112.15423/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 36 references that are in the map.
- First posted on arXiv 31 Dec 2021.

## Builds on (most cited first, 13 of 13)

- [Tensor SVD: Statistical and Computational Limits](https://mlsanity.com/paper/1703.02724/) (2017)
- [Guaranteed Non-Orthogonal Tensor Decomposition via Alternating Rank-1 Updates](https://mlsanity.com/paper/1402.5180/) (2014)
- [Factor Models for High-Dimensional Tensor Time Series](https://mlsanity.com/paper/1905.07530/) (2019)
- [Autoregressive Models for Matrix-Valued Time Series](https://mlsanity.com/paper/1812.08916/) (2018)
- [Provable Sparse Tensor Decomposition](https://mlsanity.com/paper/1502.01425/) (2015)
- [Constrained Factor Models for High-Dimensional Matrix-Variate Time Series](https://mlsanity.com/paper/1710.06075/) (2017)
- [CP Factor Model for Dynamic Tensors](https://mlsanity.com/paper/2110.15517/) (2021)
- [Factor Models for Matrix-Valued High-Dimensional Time Series](https://mlsanity.com/paper/1610.01889/) (2016)
- [Modeling Dynamic Transport Network with Matrix Factor Models: with an Application to International Trade Flow](https://mlsanity.com/paper/1901.00769/) (2019)
- [Tensor Principal Component Analysis in High Dimensional CP Models](https://mlsanity.com/paper/2108.04428/) (2021)
- [Simultaneous Decorrelation of Matrix Time Series](https://mlsanity.com/paper/2103.09411/) (2021)
- [Principal component analysis for second-order stationary vector time series](https://mlsanity.com/paper/1410.2323/) (2014)
- [Optimal covariance matrix estimation for high-dimensional noise in high-frequency data](https://mlsanity.com/paper/1812.08217/) (2018)

## Built on by (most cited first, 5 of 5)

- [Tucker Diffusion Model for High-dimensional Tensor Generation](https://mlsanity.com/paper/2604.00481/) (2026)
- [TEAFormers: TEnsor-Augmented Transformers for Multi-Dimensional Time Series Forecasting](https://mlsanity.com/paper/2410.20439/) (2024)
- [Time Series Generative Learning with Application to Brain Imaging Analysis](https://mlsanity.com/paper/2407.14003/) (2024)
- [Sparsity-Induced Global Matrix Autoregressive Model with Auxiliary Network Data](https://mlsanity.com/paper/2503.08579/) (2025)
- [MINT: Tensor Decomposition on Stacked Recurrence Matrices for Time Series Data Mining](https://mlsanity.com/paper/2608.04157/) (2026)

## Abstract (arXiv)

We consider to model matrix time series based on a tensor CP-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further refined approach which projects it into a lower-dimensional full-ranked eigenequation. This refined method improves significantly the finite-sample performance of the estimation. The asymptotic theory has been established under a general setting without the stationarity. It shows, for example, that all the component coefficient vectors in the CP-decomposition are estimated consistently with certain convergence rates. The proposed model and the estimation method are also illustrated with both simulated and real data; showing effective dimension-reduction in modelling and forecasting matrix time series.