On the Impact of Serial Dependence on Penalized Regression Methods

TL;DR

This paper investigates how serial dependence in covariates affects penalized regression estimation errors, revealing the impact of cross-correlation and proposing a pre-whitening method to improve accuracy and forecasting in time series analysis.

Contribution

It provides analytical insights into serial dependence effects on penalized regressions and introduces a novel pre-whitening procedure to mitigate spurious correlations in time series data.

Findings

Serial dependence can cause high spurious correlations in covariates.

Pre-whitening reduces estimation error and improves forecasting accuracy.

The proposed method is validated through simulations and macroeconomic data.

Abstract

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.