Applying Hybrid ARIMA-GARCH Models with Three Error Distributions for Modeling Oil Prices in Libya and Algeria

Abstract

This study analyzes the statistical properties of monthly domestic crude oil prices in Libya and Algeria from January 1983 to June 2025, aiming to model and forecast price dynamics. For modeling purposes, hybrid models combining the Autoregressive Integrated Moving Average (ARIMA) model and the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model with normal, Student-t, and GED error distributions are employed. Series stationarity is assessed using ADF tests, and model selection uses AIC and SIC criteria, with diagnostic checks for residual including Ljung-Box tests, ARCH effects, and normality assessments. Results indicate that the prices series are non-stationary, while the log-differenced series are stationary. Among candidate ARIMA models, ARIMA(0,1,1) and ARIMA(1,1,1) provide the best fit. Including conditional heteroskedasticity, ARIMA-GARCH(1,0) with Student-t distribution produces stable residuals and significant parameters estimates. Out-of-sample evaluation using RMSE and MAE identifies ARIMA(1,1,1)-GARCH(1,0)-t as the most accurate forecasting model. These findings highlight the importance of heavy-tailed error distributions and volatility clustering in modeling domestic oil price dynamics, and demonstrating that the ARIMA-GARCH models provide reliable short-term forecasting efficiency, and contribute to supporting economic and policymakers in the two countries under study.