We explore inference within sparse linear models, focusing on scenarios where both predictors and errors carry serial correlations. We establish a clear link between predictor serial correlation and the finite sample performance of the LASSO, showing that even orthogonal or weakly correlated stationary AR processes can lead to significant spurious correlations due to their serial correlations. To address this challenge, we propose a novel approach named ARMAr-LASSO (ARMA residuals LASSO), which applies the LASSO to predictor time series that have been pre-whitened with ARMA filters and lags of dependent variable. Utilizing the near-epoch dependence framework, we derive both asymptotic results and oracle inequalities for the ARMAr-LASSO, and demonstrate that it effectively reduces estimation errors while also providing an effective forecasting and feature selection strategy. Our findings are supported by extensive simulations and an application to real-world macroeconomic data, which highlight the superior performance of the ARMAr-LASSO for handling sparse linear models in the context of time series.

翻译：本文探讨了稀疏线性模型中的推断问题，重点关注预测变量和误差项均存在序列相关性的情形。我们建立了预测变量序列相关性与LASSO有限样本性能之间的明确联系，结果表明即使正交或弱相关的平稳AR过程，由于其序列相关性也可能导致显著的伪相关性。为应对这一挑战，我们提出了一种名为ARMAr-LASSO（ARMA残差LASSO）的新方法，该方法将LASSO应用于经过ARMA滤波器和因变量滞后项预白化的预测变量时间序列。利用近时点依赖性框架，我们推导了ARMAr-LASSO的渐近结果和Oracle不等式，并证明该方法能有效降低估计误差，同时提供有效的预测和特征选择策略。通过大量模拟实验和真实宏观经济数据的应用，我们的研究结果得到验证，这些实证分析突显了ARMAr-LASSO在处理时间序列背景下稀疏线性模型方面的优越性能。