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

TL;DR

This paper introduces modified estimation methods for symmetric stable ARMA and GARCH models, demonstrating their effectiveness through simulations and application to financial data.

Contribution

It presents novel modified estimation techniques for symmetric stable ARMA and GARCH models, enhancing accuracy and simplicity over existing methods.

Findings

Methods are efficient and accurate based on Monte-Carlo simulations.

Proposed techniques outperform traditional estimators in stability and precision.

Application to financial data shows practical utility of the methods.

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.