On the LAD estimation and likelihood ratio test for time series models

This thesis proposes the global self-weighted least absolute deviation (LAD) estimator for finite and infinite variance ARMA models and the global self-weighted quasi-maximum exponential likelihood estimator (QMELE) for the ARMA-GARCH models, respectively. The strong consistency and the asymptotic normality of the global self-weighted LAD and QMELE are obtained. As far as we know, the asymptotic theory of these estimators is established in the literature for the first time. The technique developed in this thesis is not standard and can be used for other time series models. Empirical studies show that these estimators have a good performance especially for heavy tailed innovations.;This thesis also investigates a likelihood ratio (LR) test for the structural change of an AR(p) model to a threshold AR(p) model. Under the null hypothesis, the limiting distribution of the LR test is the maxima of a two-parameter vector Gaussian process. When the errors are normal, the limiting distribution is parameter-free, and its percentages are tabulated via a Monte Carlo method. Simulation studies are carried out to access the performance of the LR test in the finite sample and a real example is given.