(untitled) (المجلة الدولية للبحوث العلمية, 2024)
The interest in the topic of time series forecasting has increased during the recent years and thus appeared specific modern methods, for example Autoregressive Fractional Integrated Moving Average model (ARFIMA), or what is called long memory model, which use fractionally difference (d) instead of integer which used in ARIMA models. In this study we displayed long memory feature and its tests. Our discussion supported by analysing the real time series (daily closing index of the Saudi Arabia Stock Market prices) over period 1/1/2018 to 19/12/2022, including 1240 observations, to make a good model to giving forecast results for future, using statistical tests and statistical software (R- 4.2.2 program). Firstly we checked that the data series was unstable by testing unit root, using Dickey fuller and Philips Perron tests ; and confirmed the presence of a long memory pattern in it by calculating the Hurst exponent (H), then calculated the fractional differential coefficient (d), determined the appropriate models for analysis and prediction, then the best model was chosen among them based on the comparison criteria, then predicted the values for the next 5 days, R - 4.2.2 software was used in all of these tests and predictions Statistical results indicated that the optimal model to represent the data series is ARFIMA (3,0.383,2) which used to predict future values.