Exponential Generalized Autoregressive Conditional Heteroscedastic Time Series Model Analysis with Wavelets

Data noise is one of the problems facing the accuracy of building time series models, such as the EGARCH model. In this article, it was proposed to treat the noisy data of the Exponential Generalized Autoregressive Conditional Heteroscedastic Time Series Model using wavelet analysis through wavelets (Daubechies, Coiflets, and Symlets), with a Universal thresholding and the application of a soft threshold rule. The efficiency and accuracy of the estimated parameters of the Exponential Generalized Autoregressive Conditional Heteroscedastic model (for unprocessed data from noise) were compared with the three proposed models using the Akaike and Bayesian information criteria by studying simulation data and real data based on a program in the MATLAB language designed for this purpose. The research results demonstrated that the proposed methods were more efficient than the ordinary Exponential Generalized Autoregressive Conditional Heteroscedastic model.