Lasso-based Variable Selection of ARMA Models

Abstract

This study considers a least absolute shrinkage and selection operator (Lasso)-based approach to variable selection of ARMA models. We first show that the Lasso estimator follows the Knight-Fu's limit distribution under a general tuning parameter assumption. With a special restriction on the tuning parameters, we show that the Lasso estimator achieves the "oracle" properties: zero parameters are estimated to be zero exactly, and other estimators are as efficient as those under the true model. The results are extended further for nonstationary ARMA models, and an algorithm is presented. In particular, we propose a data-driven information criterion to select the tuning parameter that is shown to be consistent with probability approaching one. A simulation study is carried out to assess the performance of the proposed procedure, and an example is provided to demonstrate its applicability.