This paper considers wavelet based estimates for the Self Similar parameters of the Linear Fractional Stable Motions.
The Consistency of the estimators is also studied. We obtain some statistical
results for the Hurst parameter estimation of Fractionally Integrated Auto Regressive Moving Average, FARIMA, time Series with Stable innovations. We also consider a class of Locally Self Similar
processes called linear linear Multifractional Stable Motions, which extends Multifractional Brownian Motion and provide where the distributions can have Heavy tail and be non-symmetric. New results for Multifractional Brownian Motion are obtained.