This paper characterizes the impact of covariate serial dependence on the non-asymptotic estimation error bound of penalized regressions (PRs). Focusing on the direct relationship between the degree of cross-correlation between covariates and the estimation error bound of PRs, we show that orthogonal or weakly cross-correlated stationary AR processes can exhibit high spurious correlations caused by serial dependence. We provide analytical results on the distribution of the sample cross-correlation in the case of two orthogonal Gaussian AR(1) processes, and extend and validate them through an extensive simulation study. Furthermore, we introduce a new procedure to mitigate spurious correlations in a time series setting, applying PRs to pre-whitened (ARMA filtered) time series. We show that under mild assumptions our procedure allows both to reduce the estimation error and to develop an effective forecasting strategy. The estimation accuracy of our proposal is validated through additional simulations, as well as an empirical application to a large set of monthly macroeconomic time series relative to the Euro Area.

翻译：本文刻画了协变量序列依赖对惩罚回归非渐近估计误差界的影响。通过聚焦于协变量间互相关程度与惩罚回归估计误差界之间的直接关系，我们证明正交或弱互相关的平稳AR过程可能因序列依赖而产生高虚假相关性。针对两个正交高斯AR(1)过程的情形，我们提供了样本互相关分布的解析结果，并通过大规模模拟研究对其进行拓展与验证。此外，我们提出了一种新方法以减轻时间序列环境中的虚假相关性，该方法将惩罚回归应用于预白化（ARMA滤波）后的时间序列。我们证明在温和假设下，该方法既能降低估计误差，又能开发出有效的预测策略。通过额外模拟以及针对欧元区月度宏观经济时间序列大样本集的实证应用，验证了所提方法的估计精度。