Aastha Madonna Sathe

In this article, we first propose the modified Hannan–Rissanen Method for estimating the parameters of 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 with Monte-Carlo simulation. Finally, we apply our proposed methods to model the financial data.

Recent research activities in forecasting suggest that artificial neural networks can be a promising alternative to the traditional linear models. However, no single model, either linear or nonlinear is capable of obtaining the forecasts accurately. In this paper, a hybrid methodology that combines symmetric α-stable autoregressive time series and artificial neural networks is proposed. The methodology is validated through Monte-Carlo simulations. Moreover, the new method is used to model real empirical data thus showing the usefulness of heavy-tailed models supported by artificial neural networks in statistical modeling.

In this paper, we first discuss some of the well-known methods available in the literature for the estimation of the parameters of a univariate/multivariate stable distribution. Based on the available methods, a new hybrid method is proposed for the estimation of the parameters of a univariate stable distribution. The proposed method is further used for the estimation of the parameters of a strictly multivariate stable distribution. The efficiency, accuracy and simplicity of the new method is shown through Monte-Carlo simulation. Finally, we apply the proposed method to the univariate and bivariate financial data.