# High Dimensional and Banded Vector Autoregressions

arXiv: https://arxiv.org/abs/1502.07831 · HTML: https://mlsanity.com/paper/1502.07831/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2015.

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

- [Benign Overfitting in Time Series Linear Models with Over-Parameterization](https://mlsanity.com/paper/2204.08369/) (2022)
- [Sparse Generalized Yule-Walker Estimation for Large Spatio-temporal Autoregressions with an Application to NO2 Satellite Data](https://mlsanity.com/paper/2108.02864/) (2021)
- [Cluster-and-Conquer: A Framework For Time-Series Forecasting](https://mlsanity.com/paper/2110.14011/) (2021)
- [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)

## Abstract (arXiv)

We consider a class of vector autoregressive models with banded coefficient matrices. The setting represents a type of sparse structure for high-dimensional time series, though the implied autocovariance matrices are not banded. The structure is also practically meaningful when the order of component time series is arranged appropriately. The convergence rates for the estimated banded autoregressive coefficient matrices are established. We also propose a Bayesian information criterion for determining the width of the bands in the coefficient matrices, which is proved to be consistent. By exploring some approximate banded structure for the auto-covariance functions of banded vector autoregressive processes, consistent estimators for the auto-covariance matrices are constructed.