This thesis investigates the Lasso-based approach for variable selection of log-GARCH models. For estimating parameters and the order of the model simultaneously, we propose a new method by combining quasi-maximum-likelihood estimator (QMLE) with the Lasso-type of penalty. This Lasso-based QMLE for log-GARCH models is shown to be strongly consistent and has the Knight-Fu’s limiting distribution. We also show that, with a special restriction on tuning parameters, the adaptive Lasso estimator can achieve the “oracle” properties. Namely, zero parameters are estimated to be zero exactly and other estimators are as efficient as those under the true model. An algorithm is discussed for empirical implementation and a data-driven information criterion is proposed to select the tuning parameter....[ Read more ]

This thesis investigates the Lasso-based approach for variable selection of log-GARCH models. For estimating parameters and the order of the model simultaneously, we propose a new method by combining quasi-maximum-likelihood estimator (QMLE) with the Lasso-type of penalty. This Lasso-based QMLE for log-GARCH models is shown to be strongly consistent and has the Knight-Fu’s limiting distribution. We also show that, with a special restriction on tuning parameters, the adaptive Lasso estimator can achieve the “oracle” properties. Namely, zero parameters are estimated to be zero exactly and other estimators are as efficient as those under the true model. An algorithm is discussed for empirical implementation and a data-driven information criterion is proposed to select the tuning parameter. Simulation study is carried out to access the performance of our selection procedure and two empirical examples are given to illustrate the usefulness of this kind of Log-GARCH models.