On AR parameter estimation with alpha stable innovations

Several methods have been suggested for estimating the parameters of an auto-regressive (AR) process where the innovation process is an independent, identically distributed (IID) α-stable process. The performance of the proposed algorithms has been studied by simulations. We suggest a novel, maximum likelihood (ML) type method for the same problem. Actually, we suggest use of the ML estimator for the Cauchy distribution for any 1 ≤ α <2. The performance of the proposed method is studied by simulations and its superiority over the existing methods is demonstrated. The simulations have been carried out carefully so the stationarity of the resulting AR process is guaranteed.