Estimation of the Parameters of Symmetric Stable ARMA and ARMA-GARCH Models

Abstract: 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.