# Estimating Structured Vector Autoregressive Model

arXiv: https://arxiv.org/abs/1602.06606 · HTML: https://mlsanity.com/paper/1602.06606/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2016.

## Built on by (most cited first, 10 of 10)

- [Towards Long-Term Time-Series Forecasting: Feature, Pattern, and Distribution](https://mlsanity.com/paper/2301.02068/) (2023)
- [Causal Forecasting:Generalization Bounds for Autoregressive Models](https://mlsanity.com/paper/2111.09831/) (2021)
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- [Switching Autoregressive Low-rank Tensor Models](https://mlsanity.com/paper/2306.03291/) (2023)
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- [The Variational Bayesian Inference for Network Autoregression Models](https://mlsanity.com/paper/2102.09232/) (2021)
- [Minimax Estimation of Partially-Observed Vector AutoRegressions](https://mlsanity.com/paper/2106.09327/) (2021)
- [Adaptive Graph Convolutional Network Framework for Multidimensional Time Series Prediction](https://mlsanity.com/paper/2205.04885/) (2022)
- [Transfer Learning for High-dimensional Reduced Rank Time Series Models](https://mlsanity.com/paper/2504.15691/) (2025)
- [Learning Unknown Interdependencies for Decentralized Root Cause Analysis in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2602.21928/) (2026)

## Abstract (arXiv)

While considerable advances have been made in estimating high-dimensional structured models from independent data using Lasso-type models, limited progress has been made for settings when the samples are dependent. We consider estimating structured VAR (vector auto-regressive models), where the structure can be captured by any suitable norm, e.g., Lasso, group Lasso, order weighted Lasso, sparse group Lasso, etc. In VAR setting with correlated noise, although there is strong dependence over time and covariates, we establish bounds on the non-asymptotic estimation error of structured VAR parameters. Surprisingly, the estimation error is of the same order as that of the corresponding Lasso-type estimator with independent samples, and the analysis holds for any norm. Our analysis relies on results in generic chaining, sub-exponential martingales, and spectral representation of VAR models. Experimental results on synthetic data with a variety of structures as well as real aviation data are presented, validating theoretical results.