Empirical Likelihood Estimation for a Class of Stable Processes

We investigate the empirical likelihood estimation for a parameter of linear processes whose innovations have i.i.d. symmetric α-stable distributions. To construct the estimating function for the empirical likelihood method, we make use of the empirical and theoretical characteristic functions. The asymptotic normality of the maximum empirical likelihood estimator is derived. The behavior of the asymptotic variance with respect to infinitesimal perturbations of the dependence effect is studied and we find that it is dependence robust when α > 1. Numerical studies are also given.