Analysis and Evaluation of ARIMA and SARIMA Models Performance in Time Series Forecasting: An Applied Study

Abstract

This study aims to analyze and evaluate the performance of ARIMA and SARIMA models in forecasting the time series of oil production in Libya, with a focus on comparing the prediction accuracy of both models and their ability to capture temporal and seasonal patterns. The research involves determining the optimal values of model parameters (p, d, q) and assessing the quality of forecast residuals using statistical tests such as the Ljung-Box test.A descriptive-analytical approach was adopted, where monthly oil production data from six oil fields was collected for the period from September 1986 to April 2014, totaling 330 observations. The characteristics of the time series were analyzed, and stationarity was tested using the Augmented Dickey-Fuller (ADF) test. The models were developed using techniques such as Grid Search and selection criteria AIC/BIC, and their performance was evaluated based on RMSE, MAE, and MAPE metrics. The results demonstrated that the SARIMA model outperformed the ARIMA model in capturing seasonal patterns. The randomness of the forecast residuals was also verified to ensure prediction quality. The study recommends removing the constant term from the model due to its insignificance and emphasizes the importance of incorporating seasonal effects to enhance prediction accuracy while monitoring model stability over time. Furthermore, the study suggests testing additional lags using ACF and PACF to refine the selection of (p, q) values and adopting the SARIMA model when clear seasonal cycles are present. Additionally, the research advises leveraging advanced techniques such as Grid Search and Bayesian Optimization for optimal parameter tuning and exploring more advanced models like SARIMA-X and hybrid models to improve forecasting accuracy.