On estimation and testing goodness of fit for m-dependent stable sequences

A class of estimators of the characteristic index of m-dependent stable sequences is proposed. The estimators are shown to be consistent and asymptotically normal. In addition, a class of goodness-of-fit tests for stability is also obtained. The performance of the estimators and the goodness-of-fit tests is evaluated through a simulation study. One of the estimators is shown to have a reasonably high relative efficiency which is uniformly superior to that of the regression estimator, which is currently most widely used. Our results have significance for modelling financial data like stock returns which have thick tailed distributions and exhibit non-linear behaviour.