On the impact of serial dependence on penalized regression methods

This paper characterizes the impact of covariates 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 correlations caused by serial dependence. In this respect, we study analytically the density of sample cross-correlations in the case of two orthogonal Gaussian AR(1) processes. Our results are validated by an extensive simulation study. Furthermore, we introduce a new procedure to remedy spurious correlations in a time series regime, applying PRs to pre-whitened (ARMA filter) 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 by means of simulations and an empirical application based on a large monthly macroeconomic data relative to the Euro Area economy.