Consistent tests for symmetric stability with finite mean based on the empirical characteristic function

In this paper we study a class of goodness-of-fit tests for the symmetric stable distribution. The proposed tests are based on a weighted integral involving the empirical characteristic function, corresponding to suitably centered data. The consistency of the tests is investigated under a moment assumption. Also, as the decay of the weight function tends to infinity, limit statistics are obtained. Our method is applied on real and simulated data.