Hypothesis test in long-range dependence processes with stable innovations

Abstract

The main objetive of this paper is to analyze hypothesis tests for the stability parameter of the stable innovations, which determines the heaviness of the distribution's tails. We will consider both a simple z-test and also the likelihood ratio test. Power analysis for both situations will be studied as well. Four estimators for the long-range dependence parameter d will be used, including parametric and semi-parametric procedures with robust versions. Three di erent estimators for the tail index will be considered in this work. A Monte Carlo study will be presented, as well as an application to real data.