Adaptative LASSO estimation for ARDL models with GARCH innovations

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 estimator is oracle, meaning that its distribution converges to the same distribution of the oracle assisted least squares, i.e., the least squares estimator calculated as if we knew the set of relevant variables beforehand. Finally, we show that the LASSO estimator can be used to construct the initial weights. The performance of the method in finite samples is illustrated using Monte Carlo simulation