Regularization Parameter Selection via Cross-Validation in the Presence of Dependent Regressors: A Simulation Study

Abstract

This letter reveals using simulation studies that regularization parameter selection via cross-validation (CV) in penalized regressions (e.g., Lasso) is valid even if the regressors are weakly dependent. In CV procedure, the time series structure of the data set is broken, meaning that there may occur a fatal problem unless the sample is i.i.d.; the estimation accuracy in the training step could be worse due to corruption of data continuity, which may furthermore lead to a bad choice of the regularization parameter. Even in such a situation, we find that CV works well as long as the sample size grows. These findings encourage us to apply the selection procedure via CV to macroeconomic empirical analyses with dependent regressors.