# Regularized Estimation of High-Dimensional Vector AutoRegressions with Weakly Dependent Innovations

arXiv: https://arxiv.org/abs/1912.09002 · HTML: https://mlsanity.com/paper/1912.09002/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2019.

## 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)
- [Concentration inequalities for high-dimensional linear processes with dependent innovations](https://mlsanity.com/paper/2307.12395/) (2023)
- [Econometrics of Machine Learning Methods in Economic Forecasting](https://mlsanity.com/paper/2308.10993/) (2023)
- [Lag selection and estimation of stable parameters for multiple autoregressive processes through convex programming](https://mlsanity.com/paper/2303.02114/) (2023)

## Abstract (arXiv)

There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive models with heavy tailed, weakly dependent innovations with virtually no assumption on the conditional heteroskedasticity. In contrast to current literature, our innovation process satisfy an L1 mixingale type condition on the centered conditional covariance matrices. This condition covers L1-NED sequences and strong (α-) mixing sequences as particular examples.