  In this article, we first propose the modified Hannan-Rissanen Method for
estimating the parameters of the autoregressive moving average (ARMA) process
with symmetric stable noise and symmetric stable generalized autoregressive
conditional heteroskedastic (GARCH) noise. Next, we propose the modified
empirical characteristic function method for the estimation of GARCH parameters
with symmetric stable noise. Further, we show the efficiency, accuracy, and
simplicity of our methods through Monte-Carlo simulation. Finally, we apply our
proposed methods to model financial data.
