In this paper, we consider parameter estimation for a stochastic process observed at some discrete times that is a solution of a given class of stochastic differential equations driven by stable processes. Firstly, we consider the diffusion coefficients parameters estimation problem such as the scaling parameter and the driving stable process parameters. Secondly, we address the question of the joint estimation with the drift coefficients for Stable driven Cox-Ingersoll-Ross and Ornstein-Uhlenbeck processes. Our methodology which is based on the use of Nadaraya-Watson estimator is new according to the literature of such estimation problem. Indeed it is based on a combination of the characteristic sample function and the (linear or weighted) regression methods. We discuss the validity and efficiency of the numeric implementation of the estimators on synthetic data and real financial data as indexes and exchange rates. As a forthcoming work, we intend to provide a package (in the R programming language) for this type of estimation problem.