Joint robust parameter estimation for symmetric stable distributions

In this paper we present a robust parameter estimation method for jointly estimating shape parameter α, scale parameter γ and location parameter δ of a symmetric stable distribution. The proposed estimation method is based on Probability Integral Transformation (PIT) and robust M-estimators. The procedure is ready to use as besides the theoretical description we provide the numerical algorithm and all constants and approximations of functions necessary to compute the estimators. Robust characteristics and the asymptotic behaviour of estimator α is investigated. A simulation sequence was carried out to examine statistical properties of the estimator α. We perform an application for a data set of returns of some assets listed in Budapest Stock Exchange.