Assessing Models Behaviors and the Forecasting Performance of Arima and Garch Models: An Empirical Study

This study investigates the statistical properties, volatility dynamics, and forecasting performance of crude oil returns using a comprehensive time series modeling approach. Descriptive analyses reveal that returns are centered around zero with small negative averages, exhibiting pronounced volatility clustering and episodes of extreme deviations driven by geopolitical and macroeconomic shocks. Diagnostic tests confirm the presence of nonlinear dependence and heteroskedasticity, making models such as GARCH suitable for capturing the persistent volatility patterns. Stationarity of the return series supports the application of ARIMA and GARCH-based models, which effectively accommodate the complex features observed in the data. Model selection across varying sample sizes consistently favors parsimonious ARIMA(0,0,q) structures with no autoregressive terms, while GARCH(1,1) captures the high volatility persistence evident in the market. Forecasting evaluations demonstrate that model accuracy improves with larger datasets, with combined ARIMA-GARCH models, especially those with higher-order ARIMA specifications, outperforming simpler models in larger samples. The findings underscore the importance of incorporating volatility modeling and selecting appropriate model complexity based on data availability to enhance forecast precision. Overall, the results provide valuable insights into the dynamics of crude oil prices and offer robust guidance for modeling and forecasting in volatile energy markets.