Regression Coecient and Autoregressive Order Shrinkage and Selection via the RA-lasso

Abstract: The least absolute shrinkage and selection operator (lasso) has been widely used in regression shrinkage and selection. However, the lasso is not designed to take into account the autoregressive process in a nested fashion. In this article, we propose the regression and autocorrelated lasso (RA-lasso) to jointly shrink the regression and the nested autocorrelated coecients in the REGression model with AutoRegressive errors (REGAR). We show that the RA-lasso estimator performs as well as the oracle estimator (i.e., it works as well as if the correct submodel were known). Our extensive simulation studies demonstrate that the RA-lasso outperforms the lasso. An empirical example is also presented to illustrate the usefulness of RA-lasso. Finally, the extension of RA-lasso to the autoregression with exogenous variables (ARX) is discussed. Reference