~35~ International Journal of Statistics and Applied Mathematics 2025; 10(2): 35-45 ISSN: 2456-1452 Maths 2025; 10(2): 35-45 © 2025 Stats & Maths https://www.mathsjournal.com Received: 09-12-2024 Accepted: 18-01-2025 Ahmed Ali Salman Lecturer, College of Administration and Economics, Al-Iraqia University, Iraq Ansseif A Latif Ansseif Assistant Professor, College of Administration and Economics, Al-Iraqia University, Iraq Corresponding Author: Ahmed Ali Salman Lecturer, College of Administration and Economics, Al-Iraqia University, Iraq Modeling and forecasting volatility in the Iraq stock exchange: A survey study using ARCH and GARCH models Ahmed Ali Salman and Ansseif A Latif Ansseif DOI: https://dx.doi.org/10.22271/maths.2025.v10.i2a.1978 Abstract This study aimed at the effectiveness of self-regression models conditional on the instability of variance ARCH in predicting the returns of shares traded for the Iraq Stock Exchange, in addition to the possibility of proposing a model in providing predictions with relatively small errors during the period from 5/1/2021 to 18/10/2024 by daily observations over the studied period, and to achieve the objectives of the study, the daily closing price was calculated as an indicator to predict fluctuations and estimate self-regression conditional on the instability of variance based on self-regression models conditional on heterogeneity variance. ARCH:"Auto Regressive Conditional Heteroscedasticity" and GARCH: "Generalized Auto Regressive Conditional Heteroscedasticity" are intended to model variance in data that have different fluctuations (different variability) in time series periods, i.e. have high variance sometimes and low variance across different time periods of the time series. For financial analysts, these patterns promise a period of wild and calm. Keywords: GARCH-ARCH patterns, stock market index, closing price, forecast Introduction The Iraq stock exchange is of economic importance to financial institutions and companies, as it provides regulations and means that contribute to achieving justice, efficiency and transparency for financial transactions within the market, as it provides a reliable and reliable financial time series under which the investment decision-making process is carried out. as the financial time series has time periods of variations and turns due to the complex characteristics that characterize it, in addition to its unexpected random movement over time, which increases the uncertainty and makes predicting its metabolite trends accurately faces difficulty (Zakaria &abdalla: 2012) [22] , and given the important role of predicting fluctuations and metabolite fluctuations of the stock market index traded on a daily basis in the investment decision-making process, which in turn requires the use of quantitative analytical models through which a mathematical model can be formulated that fits with the nature of the financial time series on the one hand and is able to predict metabolic trends (Caporin and Storti: 2020) [8] . The paragraph aims to see what has been adhered to by researchers and their findings within the field of research, for the purpose of enriching the subject of research and obtaining knowledge accumulation: (Brodocianu: 2015) [6] The study was conducted in the field of financial market return modeling, which aimed to analyze the CAC40 index and the European Euro Eurinext 100 index using autoregressive models conditional on instability of variance ARCH, for a period of ten previous years, and the study confirmed the importance of diversification in increasing returns and reducing risks, and the study also confirmed that due to the instability of the variation of financial chains of both indicators, the predictive model, which was confirmed to determine the shocks witnessed by these two indicators, is the regression model. Self-conditioned by the instability of exponential Generalized ARCH (EGARCH). (Benelbar, 2021) [4] The aim of this article is to study the possibility of modeling