Asymptotics of the Adaptive Elastic Net Estimation for Conditional Heteroscedastic Time Series Models

Abstract

In this paper we propose an iteratively reweighted adaptive elastic net estimation method for conditional heteroscedastic time series models. The sign consistency and the asymptotic normality of the estimator are investigated. Compared with the Lasso method, the elastic net is more efficient for autoregressive time series models, because it benefits not only from the selection of the Lasso but also from the grouping effect inherited from the ridge penalty. The Monte Carlo simulation studies based on an AR-ARCH model are reported to assess the finite-sample performance of the proposed elastic net method.