# On LASSO for High Dimensional Predictive Regression

arXiv: https://arxiv.org/abs/2212.07052 · HTML: https://mlsanity.com/paper/2212.07052/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 74 references that are in the map.
- First posted on arXiv 14 Dec 2022.

## Builds on (most cited first, 8 of 8)

- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [High-Dimensional Granger Causality Tests with an Application to VIX and News](https://mlsanity.com/paper/1912.06307/) (2019)
- [Oracle Inequalities for High Dimensional Vector Autoregressions](https://mlsanity.com/paper/1311.0811/) (2013)
- [Boosting High Dimensional Predictive Regressions with Time Varying Parameters](https://mlsanity.com/paper/1910.03109/) (2019)
- [The boosted HP filter is more general than you might think](https://mlsanity.com/paper/2209.09810/) (2022)
- [Identifying Cointegration by Eigenanalysis](https://mlsanity.com/paper/1505.00821/) (2015)
- [An Automated Approach Towards Sparse Single-Equation Cointegration Modelling](https://mlsanity.com/paper/1809.08889/) (2018)
- [Predictive Quantile Regression with Mixed Roots and Increasing Dimensions: The ALQR Approach](https://mlsanity.com/paper/2101.11568/) (2021)

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

- [Deconfounded Warm-Start Thompson Sampling with Applications to Precision Medicine](https://mlsanity.com/paper/2505.17283/) (2025)

## Abstract (arXiv)

This paper examines LASSO, a widely-used L1-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors are present. The consistency of LASSO is contingent upon two key components: the deviation bound of the cross product of the regressors and the error term, and the restricted eigenvalue of the Gram matrix. We present new probabilistic bounds for these components, suggesting that LASSO's rates of convergence are different from those typically observed in cross-sectional cases. When applied to a mixture of stationary, nonstationary, and cointegrated predictors, LASSO maintains its asymptotic guarantee if predictors are scale-standardized. Leveraging machine learning and macroeconomic domain expertise, LASSO demonstrates strong performance in forecasting the unemployment rate, as evidenced by its application to the FRED-MD database.