In this paper we show the validity of the adaptive LASSO procedure in estimating stationary ARDL(p,q) models with GARCH innovations. We show that, given a set of initial weights, the adaptive Lasso selects the relevant variables with probability converging to one. Afterwards, we show that the...

We study the asymptotic properties of the Adaptive LASSO (adaLASSO) in sparse, high-dimensional, linear time-series models. We assume that both the number of covariates in the model and the number of candidate variables can increase with the sample size (polynomially or geometrically). In other...