# High-dimensional vector autoregressive time series modeling via tensor decomposition

arXiv: https://arxiv.org/abs/1909.06624 · HTML: https://mlsanity.com/paper/1909.06624/

## Key facts

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

## Built on by (most cited first, 14 of 14)

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- [Enabling Tensor Decomposition for Time-Series Classification via A Simple Pseudo-Laplacian Contrast](https://mlsanity.com/paper/2409.15200/) (2024)
- [Sparsity-Induced Global Matrix Autoregressive Model with Auxiliary Network Data](https://mlsanity.com/paper/2503.08579/) (2025)
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- [The Cost of Long Memory: State, Context, and Stability Complexity in Sequence Models](https://mlsanity.com/paper/2610.08816/) (2026)

## Abstract (arXiv)

The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to rearrange the transition matrices of the model into a tensor form such that the parameter space can be restricted along three directions simultaneously via tensor decomposition. In contrast, the reduced-rank regression method can restrict the parameter space in only one direction. Besides achieving substantial dimension reduction, the proposed model is interpretable from the factor modeling perspective. Moreover, to handle high-dimensional time series, this paper considers imposing sparsity on factor matrices to improve the model interpretability and estimation efficiency, which leads to a sparsity-inducing estimator. For the low-dimensional case, we derive asymptotic properties of the proposed least squares estimator and introduce an alternating least squares algorithm. For the high-dimensional case, we establish non-asymptotic properties of the sparsity-inducing estimator and propose an ADMM algorithm for regularized estimation. Simulation experiments and a real data example demonstrate the advantages of the proposed approach over various existing methods.