Simulation experiments are a means of solving in many fields, and it is the process of designing a model of the real system in order to follow it and identify its behavior through certain models and formulas written according to a repeating software style with a number of iterations. The aim of this study is to build a model that deals with the behavior suffering from the state of (heteroskedasticity) by studying the models (APGARCH & NAGARCH) using (Gaussian) and (Non-Gaussian) distributions for different sample sizes (500,1000,1500,2000) through the stage of time series analysis (identification , estimation, diagnostic checking and prediction). The data was generated using the estimations of the parameters resulting from the application of these models to the return series for the exchange rates of Iraqi dinar against US dollar (IQ/USD) for the period from (21/7/2011) until (21/07/2021) and then using these estimations in the process of generating data. The identifications were made using the (Ljung-Box and ARCH tests) with (1000 replicates) and the result showed the presence of states (autocorrelation and heteroskedasticity) and this states increased with increasing the sample size and the best result of NAGARCH with Normal distribution and the best result of APGARCH with General error distribution. The Maximum Likelihood Estimation method used to estimate the parameters of the models and the best result with largest sample size (2000) , in the diagnostic checking phase the result showed the ability of the models (NAGARCH & APGARCH) to process the states of (autocorrelation and heteroskedasticity) and the best result with (APGARCH) model when the error distributed (General error distribution)
