# Concentration inequalities for high-dimensional linear processes with dependent innovations

arXiv: https://arxiv.org/abs/2307.12395 · HTML: https://mlsanity.com/paper/2307.12395/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 59 references that are in the map.
- First posted on arXiv 23 Jul 2023.

## Builds on (most cited first, 15 of 15)

- [Machine Learning Advances for Time Series Forecasting](https://mlsanity.com/paper/2012.12802/) (2020)
- [Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regression](https://mlsanity.com/paper/1804.02605/) (2018)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Concentration Inequalities for Statistical Inference](https://mlsanity.com/paper/2011.02258/) (2020)
- [Oracle Inequalities for High Dimensional Vector Autoregressions](https://mlsanity.com/paper/1311.0811/) (2013)
- [Sharper Sub-Weibull Concentrations](https://mlsanity.com/paper/2102.02450/) (2021)
- [Bridging factor and sparse models](https://mlsanity.com/paper/2102.11341/) (2021)
- [A Direct Estimation of High Dimensional Stationary Vector Autoregressions](https://mlsanity.com/paper/1307.0293/) (2013)
- [Regularized Estimation of High-Dimensional Vector AutoRegressions with Weakly Dependent Innovations](https://mlsanity.com/paper/1912.09002/) (2019)
- [Rate-Optimal Robust Estimation of High-Dimensional Vector Autoregressive Models](https://mlsanity.com/paper/2107.11002/) (2021)
- [Sparse Identification and Estimation of Large-Scale Vector AutoRegressive Moving Averages](https://mlsanity.com/paper/1707.09208/) (2017)
- [Bootstrap Based Inference for Sparse High-Dimensional Time Series Models](https://mlsanity.com/paper/1806.11083/) (2018)
- [A Survey of Estimation Methods for Sparse High-dimensional Time Series Models](https://mlsanity.com/paper/2107.14754/) (2021)
- [Sparse Generalized Yule-Walker Estimation for Large Spatio-temporal Autoregressions with an Application to NO2 Satellite Data](https://mlsanity.com/paper/2108.02864/) (2021)
- [Sparse High-Dimensional Vector Autoregressive Bootstrap](https://mlsanity.com/paper/2302.01233/) (2023)

## Built on by (most cited first, 1 of 1)

- [Tail-Aware Information-Theoretic Bounds for LLM Alignment under Heavy-Tailed Rewards](https://mlsanity.com/paper/2604.10727/) (2026)

## Abstract (arXiv)

We develop concentration inequalities for the l_∞ norm of vector linear processes with sub-Weibull, mixingale innovations. This inequality is used to obtain a concentration bound for the maximum entrywise norm of the lag-h autocovariance matrix of linear processes. We apply these inequalities to sparse estimation of large-dimensional VAR(p) systems and heterocedasticity and autocorrelation consistent (HAC) high-dimensional covariance estimation.