This paper characterizes the impact of serial dependence on the non-asymptotic estimation error bound of penalized regressions (PRs). Focusing on the direct relationship between the degree of cross-correlation of covariates and the estimation error bound of PRs, we show that orthogonal or weakly cross-correlated stationary AR processes can exhibit high spurious cross-correlations caused by serial dependence. In this respect, we study analytically the density of sample cross-correlations in the simplest case of two orthogonal Gaussian AR(1) processes. Simulations show that our results can be extended to the general case of weakly cross-correlated non Gaussian AR processes of any autoregressive order. To improve the estimation performance of PRs in a time series regime, we propose an approach based on applying PRs to the residuals of ARMA models fit on the observed time series. We show that under mild assumptions the proposed approach allows us both to reduce the estimation error and to develop an effective forecasting strategy. The estimation accuracy of our proposal is numerically evaluated through simulations. To assess the effectiveness of the forecasting strategy, we provide the results of an empirical application to monthly macroeconomic data relative to the Euro Area economy.

中文翻译：

---

关于序列依赖对惩罚回归方法的影响

本文描述了序列依赖对惩罚回归 (PRs) 的非渐近估计误差界的影响。着眼于协变量的互相关程度与 PR 的估计误差界限之间的直接关系，我们表明正交或弱互相关的平稳 AR 过程可以表现出由序列依赖性引起的高虚假互相关。在这方面，我们分析研究了两个正交高斯 AR(1) 过程的最简单情况下样本互相关的密度。模拟表明，我们的结果可以扩展到任何自回归阶的弱互相关非高斯 AR 过程的一般情况。为了提高时间序列机制中 PR 的估计性能，我们提出了一种基于将 PR 应用于符合观察到的时间序列的 ARMA 模型的残差的方法。我们表明，在温和的假设下，所提出的方法允许我们减少估计误差并制定有效的预测策略。我们建议的估计精度通过模拟进行数值评估。为了评估预测策略的有效性，我们提供了与欧元区经济相关的月度宏观经济数据的实证应用结果。