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.

ARIMA, GARCH, Forecasting, Volatility, Parsimonious, Financial, Crude Oil.

1. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327. doi:10.1016/0304-4076(86)90063-1 [Google Scholar] [Crossref]

2. Box, G.E.P. and Jenkins, G.M. (1976) Time Series Analysis: Forecasting and Control. Revised Edition, Holden Day, San Francisco. [Google Scholar] [Crossref]

3. Bunnag, T. (2024). The importance of gold’s effect on investment and predicting the world gold price using the ARIMA and ARIMA-GARCH model. Ekonomikalia Journal of Economics, 2(1), 38–52. doi:10.60084/eje.v2i1.155 [Google Scholar] [Crossref]

4. Di-Giorgi, G., Salas, R., Avaria, R., Ubal, C., Rosas, H., & Torres, R. (2025). Volatility forecasting using deep recurrent neural networks as GARCH models. Computational Statistics, 40(6), 3229–3255. doi:10.1007/s00180-023-01349-1 [Google Scholar] [Crossref]

5. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007. doi:10.2307/1912773 [Google Scholar] [Crossref]

6. Hasanov, A. S., Brooks, R., Abrorov, S., & Burkhanov, A. U. (2024). Structural breaks and GARCH models of exchange rate volatility: Re-examination and extension. Journal of Applied Econometrics, 39(7), 1403–1407. doi:10.1002/jae.3091 [Google Scholar] [Crossref]

7. Kaur, J., Parmar, K. S., & Singh, S. (2023). Autoregressive models in environmental forecasting time series: A theoretical and application review. Environmental Science and Pollution Research, 30, 19617–19641. doi:10.1007/s11356-023-25148-9 [Google Scholar] [Crossref]

8. Mbonigaba, C., Vasuki, M., Kumar, A. D., & Asamoah, P. J. (2025). Applications of GARCH models for volatility forecasting in high-frequency trading environments. International Journal of Applied and Advanced Scientific Research, 10(1), 12–21. doi:10.5281/zenodo.14904200 [Google Scholar] [Crossref]

9. Phung Duy, Q., Nguyen Thi, O., Le Thi, P. H., Pham Hoang, H. D., Luong, K. L., & Nguyen Thi, K. N. (2024). Estimating and forecasting Bitcoin daily prices using ARIMA-GARCH models. Business Analyst Journal, 45(1), 11–23. doi:10.1108/BAJ-05-2024-0027 [Google Scholar] [Crossref]

10. Rapach, D. E., & Strauss, J. K. (2008). Structural breaks and GARCH models of exchange rate volatility. Journal of Applied Econometrics, 23(1), 65–90. doi:10.1002/jae.976 [Google Scholar] [Crossref]

11. Sirisha, U. M., Belavagi, M. C., & Attigeri, G. (2024). Profit prediction using ARIMA, SARIMA and LSTM models in time series forecasting: A comparison. IEEE Access, 10, 124715–124727. doi:10.1109/ACCESS.2022.3224938 [Google Scholar] [Crossref]

• Performance Analysis of Silicon PV Array Using Infrared Thermography and Detecting Temperature Non-Uniformities
• Dynamic Capabilities and Digital Transformation Performance: The Role of Organizational Agility in the Public Sector
• Comparative Effectiveness of Neural Mobilization Versus Positional Release Technique in Cervical Radiculopathy – An Experimental Study
• Soil Moisture Mapping of Solano Nueva Vizcaya: A Comparison and Review
• Silent Assistance for Emergencies (SAFE): A Mobile-Based Emergency Reporting Application for the Deaf and Mute Community