Forecasting Nigeria’s Oil Price Volatility: A Comparative Analysis of GARCH Models and Heston’s Stochastic Models
DOI:
https://doi.org/10.54536/ajase.v4i1.4693Keywords:
EGARCH, FIGARCH, GARCH, Heston Model, IGARCH, Symmetric, TGARCHAbstract
Modeling the volatility of crude oil prices is essential because it gives substantial influence to the oil producing countries. Nigeria, the biggest oil producer in Africa and a major participant in the world oil market, has significant economic difficulties changes in oil prices. This study uses 14 years of crude oil price data (2010–2023) to assess and compare the forecasting effectiveness of the Heston stochastic volatility model and GARCH-type models (GARCH, EGARCH, IGARCH, TGARCH, and FIGARCH). According to the analysis, GARCH-type models with Student’s t-distribution perform better than models with typical innovation. With a log-likelihood value of 12022.3, an AIC of -4.7012, a mean error (ME) of 0.0254, and a root mean square error (RMSE) of 0.0534, the EGARCH model outperformed the others. Nonetheless, the Heston model outperformed all GARCH-type models in terms of forecast accuracy, achieving the smallest error (0.000564) and successfully capturing fat-tail characteristics in daily return distributions. The study indicates that the Heston model offers a better fit and more accurate forecast than GARCH-type models using data from January to December 2023 for out-of-sample forecasting. These results provide stakeholders and policymakers with important information for controlling the volatility of Nigeria’s crude oil market.
Downloads
References
Adams, S. O., Asemota, O. J., & Ibrahim, A. A. (2024). Asymmetric GARCH type models and LSTM for volatility characteristics analysis of Nigeria Stock Exchange returns. American Journal of Mathematics and Statistics, 4(2), 17–32. https://doi.org/10.5923/j.ajms.20241402.01
Adams, S. O., & Bello, J. O. (2022). Modeling the effect of crude oil production and other factors on Nigeria economy: An autoregressive distributed lag approach. Science Archives, 3(1), 72–79. http://dx.doi.org/10.47587/SA.2022.3109
Adrangi, B., Chatrath, A., Dhanda, K. K., & Raffiee, K. (2001). Chaos in oil prices? Evidence from futures markets. Energy Economics, 23(4), 405–425. https://doi.org/10.1016/s0140-9883(00)00079-7
Agnolucci, P. (2009). Volatility in crude oil futures: A comparison of the predictive ability of GARCH and implied volatility models. Energy Economics, 31(2), 316–321. https://doi.org/10.1016/j.eneco.2008.11.001
Ahmed, R. A., & Shabri, A. B. (2014). Daily Crude Oil Price Forecasting Model Using Arima, Generalized Autoregressive Conditional Heteroscedastic And Support Vector Machines. American Journal of Applied Sciences, 11(3), 425–432. https://doi.org/10.3844/ajassp.2014.425.432
Alessandri, P. &. Mumtaz. H. (2019). Financial regimes and uncertainty shocks. Journal of Monetary Economics, Elsevier, 101(C), 31-46. https://doi.org/10.1016/j.jmoneco.2018.05.001
Angelidis, T., Benos, A., & Degiannakis, S. (2004). The use of GARCH models in VaR estimation. Statistical Methodology, 1(1–2), 105–128. https://doi.org/10.1016/j.stamet.2004.08.004
Awujola., A., Adams, S.O., Alumbugu, A.I. (2015). Oil Exportation and Economic Growth in Nigeria. Developing Country Studies, 5(15), 1-15.
Bhowmik, R., & Wang, S. (2020). Stock Market Volatility and Return Analysis: A Systematic Literature Review. Entropy, 22(5), 522. https://doi.org/10.3390/e22050522
Charles, A., & Darné, O. (2021). Econometric history of the growth–volatility relationship in the USA: 1919–2017. Cliometrica, 15(2), 419-442. https://doi.org/10.1007/s11698-020-00209-y
Cheong, C. W. (2009). Modeling and forecasting crude oil markets using ARCH-type models. Energy Policy, 37(6), 2346–2355. https://doi.org/10.1016/j.enpol.2009.02.026
Clark, P. K. (1973). A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices. Econometrica, 41(1), 135–155. https://doi.org/10.2307/1913889
Chan, J. C. C., & Hsiao, C. Y. L. (2013). Estimation of stochastic volatility models with heavy tails and serial dependence (CAMA Working Paper No. 2013-74). Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University. https://ideas.repec.org/p/een/camaaa/2013-74.html
Chan, J. C. C., & Hsiao, C. Y. L. (2013). Estimation of stochastic volatility models with heavy tails and serial dependence (CAMA Working Paper No. 2013-74). Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University. http://dx.doi.org/10.2139/ssrn.2359838
Deebom, Z. D., & Essi, I. D. (2017). Modeling Price Volatility of Nigerian Crude Oil Markets Using GARCH Model: 1987-2017. International Journal of Applied Science and Mathematical Theory, 3(4).
Ding, Z., & Granger, C. W. (1996). Modeling volatility persistence of speculative returns: A new approach. Journal of Econometrics, 73(1), 185–215. https://doi.org/10.1016/0304-4076(95)01737-2
Diebold, F. X., Kilian, L., & Nerlove, M. L. (2006). Time Series Analysis. PIER Working, 28556, 06-019, http://dx.doi.org/10.2139/ssrn.910909
Dunn, S., & Holloway, J. (2012, September). The Pricing of Crude Oil. RBA Bulletin Reserve Bank of Australia, 65-74. https://www.rba.gov.au/publications/bulletin/2012/sep/pdf/bu-0912-8.pdf
Dunn, S., & Holloway, J. (2012). The Pricing of Crude Oil. Reserve Bank of Australia, 65-74. https://ideas.repec.org/a/rba/rbabul/sep2012-08.html
Ekong, C. N. and Onye, K. U. (2017): Application of Garch Models to Estimate and Predict Financial Volatility of Daily Stock Returns in Nigeria. International Journal of Managerial Studies and Research (IJMSR), 5(8), 18-34.
Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987-1007. https://doi.org/10.2307/1912773
Engle, R. F., & Lee, G. (1999). A long-run and short-run component model of stock return volatility. In R. F. Engle & H. White (Eds.), Cointegration, causality, and forecasting: A festschrift in honor of Clive W. J. Granger (pp. 475–497). Oxford University Press.
Fattouh, B., & Oxford Institute for Energy Studies. (2011). An anatomy of the crude oil pricing system (WPM 40). Oxford Institute for Energy Studies. https://www.oxfordenergy.org/wpcms/wp-content/uploads/2011/03/WPM40-AnAnatomyoftheCrudeOilPricingSystem-BassamFattouh-2011.pdf
Fondo, K. S., Onago, A. A., Kiti, L. A., & Otulo, C. W. (2021). Modeling of Petroleum Prices in Kenya Using Autoregressive Integrated Moving Average and Vector Autoregressive Models. IOSR Journal of Mathematics, 17(6), 18–27. https://doi.org/10.9790/5728-1706011827
Gasper, L., & Mbwambo, H. (2023). Forecasting Crude Oil Prices By Using ARIMA Model: Evidence From Tanzania. Journal of Accounting Finance and Auditing Studies, 9(2), 158-175. https://doi.org/10.32602/jafas.2023.017
Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. The Journal of Finance, 48(5), 1779–1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
Gokcan, S. (2000) Forecasting Volatility of Emerging Stock Markets Linear versus Non-Linear GARCH Models. Journal of Forecasting, 19, 499-504. https://doi.org/10.1002/1099-131X(200011)19:6<499::AID-FOR745>3.0.CO;2-P
Guo, H. and Kevin L. K (2005). Oil price volatility and US macroeconomic activity. Review-Federal Reserve Bank Of Saint Louis, 87, 669-684. https://doi.org/10.20955/r.87.669-84
Hammami, A., Ghenimi, A., & Bouri, A. (2019). Oil prices, US exchange rates, and stock market: Evidence from Jordan as a net oil importer. MPRA Paper No. 94570. University Library of Munich. https://ideas.repec.org/p/pra/mprapa/94570.html
Haque, M. I., Yunus, M. I., & Shaik, A. R. (2021). The Correlates of Terms of Trade in Oil Exporting Countries of Gulf Cooperation Council Region. International Journal of Energy Economics and Policy, 11(4), 543–548. Retrieved from https://www.econjournals.com/index.php/ijeep/article/view/11366
Hasanov, A. S., Shaiban, M. S., & Al-Freedi, A. (2020). Forecasting volatility in the petroleum futures markets: A re-examination and extension. Energy Economics, 86, 104626. https://doi.org/10.1016/j.eneco.2019.104626
Herrera, A. M., Hu, L., & Pastor, D. (2018). Forecasting crude oil price volatility. International Journal of Forecasting, 34(4), 622–635. https://doi.org/10.1016/j.ijforecast.2018.04.007
Knoema. (n.d.). Crude oil reserves – Nigeria. https://knoema.com/atlas/Nigeria/topics/Energy/Oil/Crude-oil-reserves
Iwayemi, A. (1992). Market structure, excess capacity and price movement: implications for the world oil market in the 1990s. OPEC Review, 16(3), 299–307. https://doi.org/10.1111/j.1468-0076.1992.tb00434.x
Kang, S. H., & Yoon, S. (2012). Modeling and forecasting the volatility of petroleum futures prices. Energy Economics, 36, 354–362. https://doi.org/10.1016/j.eneco.2012.09.01
Kang, S. H., Kang, S., & Yoon, S. (2009). Forecasting volatility of crude oil markets. Energy Economics, 31(1), 119–125. https://doi.org/10.1016/j.eneco.2008.09.006
Li, M., Keung, L. W., & Li, G. (2013). On Mixture Memory Garch Models. Journal of Time Series Analysis, 34(6), 606-624. https://doi.org/10.1111/jtsa.12037
Lux, T., Segnon, M., & Gupta, R. (2016). Forecasting crude oil price volatility and value-at-risk: Evidence from historical and recent data. Energy Economics, 56, 117–133. https://doi.org/10.1016/j.eneco.2016.03.008
Mary, I. (2003). Nigeria regains position as Africa’s largest oil producer. Premium Times. https://www.premiumtimesng.com/business/604891-nigeria-regions-position-as-africas-largest-oil-producer.html.
McMillan, D. G., & Speight, A. E. H. (2004). Daily volatility forecasts: reassessing the performance of GARCH models. Journal of Forecasting, 23(6), 449–460. https://doi.org/10.1002/for.926
Miletic, M., & Miletic, S. (2015). Performance of Value at Risk Models in the Midst of the Global Financial Crisis in Selected CEE Emerging Capital Markets. Economic Research-Ekonomska Istraživanja, 28(1), 132-166. https://doi.org/10.1080/1331677X.2015.1028243
Mohammadi, H., & Su, L. (2010). International evidence on crude oil price dynamics: Applications of ARIMA-GARCH models. Energy Economics, 32(5), 1001–1008. https://doi.org/10.1016/j.eneco.2010.04.009
Monoyios, M., & Sarno, L. (2002). Mean reversion in stock index futures markets: A nonlinear analysis. Journal of Futures Markets, 22(4), 285. https://doi.org/10.1002/fut.10008.abs
Narayan, P. K., & Narayan, S. (2007). Modelling oil price volatility. Energy Policy, 35(12), 6549–6553. https://doi.org/10.1016/j.enpol.2007.07.020
Nerlove, F. X. D. &. L. K. &. M. (2006). Time Series Analysis. ideas.repec.org. https://ideas.repec.org/p/pen/papers/06-019.html
Ng’ang’a, F. W., & Oleche, M. (2022). Modelling and Forecasting of Crude Oil Price Volatility Comparative Analysis of Volatility Models. Journal of Financial Risk Management, 11, 154-187. https://doi.org/10.4236/jfrm.2022.111008
NNPC. (2013). The future of Nigeria’s petroleum industry. Nigerian National Petroleum Corporation. https://www.nnpcgroup.com/PublicRelations/NNPCinthenews/tabid/92/articleType/ArticleView/articleId/457/The-Future-of-Nigerias-Petroleum-Industry.aspx
Nuprc. (2023). Nuprc annual report. Nigerian Upstream Petroleum Regulatory Commission. https://www.Nuprc.gov.ng/wp-content/uploads/2024/04/Updated 2023 NUPRC Annual Report
Nwachukwu, J. O. (2023, May 10). Countries with highest oil reserve revealed. Daily Post Nigeria. https://dailypost.ng/2023/05/10/countries-with-highest-oil-reserve-revealed-see-list/
Nwokeji, G. U. (2007). The Nigerian National Petroleum Corporation and the development of the Nigerian oil and gas industry: History, strategies and current directions. The James A. Baker III Institute for Public Policy, Rice University, Houston.
Odewale, A. (2023, June). Consequences of fuel subsidy removal on Nigeria’s balance of trade. Vanguard. https://www.vanguardngr.com/2023/06/consequences-of-fuel-subsidy-removal-on-nigerias-balance-of-trade/
Ozturk, S. S., & Richard, J. (2014). Stochastic volatility and leverage: Application to a panel of S&P500 stocks. Finance Research Letters, 12, 67–76. https://doi.org/10.1016/j.frl.2014.11.006
Popp, A., & Zhang, F. (2016). The macroeconomic effects of uncertainty shocks: The role of the financial channel. Journal of Economic Dynamics and Control, 69(C), 319-349. https://doi.org/10.1016/j.jedc.2016.05.021
Rodhan, M. A. (2023). The Effect of US Shale Oil Production on Local and International Oil Markets. International Journal of Energy Economics and Policy, 13(4), 433–443. https://doi.org/10.32479/ijeep.14455
Salisu, A. A., & Fasanya, I. O. (2012). Comparative Performance of Volatility Models for Oil Price. International Journal of Energy Economics and Policy, 2(3), 167–183. Retrieved from https://www.econjournals.org.tr/index.php/ijeep/article/view/235
Sadorsky, P. (1999). Oil price shocks and stock market activity. Energy Economics, 21(5), 449–469. https://doi.org/10.1016/S0140-9883(99)00020-1
Sadorsky, P. (2006). Modeling and forecasting petroleum futures volatility. Energy economics, 28 (4), 467-488. https://doi.org/10.1016/j.eneco.2006.04.005
Salisu, A. A. (2014). Modelling oil price volatility before, during and after the global financial crisis. OPEC Energy Review, 38(4), 469-495. https://doi.org/10.1111/opec.12037
Sekati, B. N., Tsoku, J. T., & Metsileng, L. D. (2020). Modelling the oil price volatility and macroeconomic variables in South Africa using the symmetric and asymmetric GARCH models, Cogent Economics & Finance. Taylor & Francis Journals, 8 (1), 1-12. https://doi.org/10.1080/23322039.2020.1792153.
Shambulingappa, H.S. (2020). Crude oil price forecasting using machine learning. International Journal of Advanced Scientific Innovation, 1(1), 1–11. https://doi.org/10.5281/zenodo.4641697
Shephard, N. (2005). Stochastic volatility. Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. https://econpapers.repec.org/paper/nufeconwp/0517.htm
Vlaar, P. J. (2000). Value at risk models for Dutch bond portfolios. Journal of Banking & Finance, 24(7), 1131–1154. https://doi.org/10.1016/s0378-4266(99)00068-0
Wang, S., Yu, L. and Lai, K.K. (2004). A novel hybrid AI system framework for crude oil price forecasting. Data Mining and Knowledge Management, 3327, 233-242. https://doi.org/10.1007/978-3-540-30537-8_26
Wang, Y., & Liu, L. (2016). Crude oil and world stock markets: volatility spillovers, dynamic correlations, and hedging. Empirical Economics, Springer, 50(4), 1481-1509. https://doi.org/10.1007/s00181-015-0983-2
Xiang, Y. (2022). Using ARIMA-GARCH Model to Analyze Fluctuation Law of International Oil Price. Mathematical Problems in Engineering, 2022, 1–7. https://doi.org/10.1155/2022/3936414
Yakubu , M., Abdullahi , M. M., Maijama’a , R., & Musa , K. S. (2023). Investigating the Effect of Petroleum Subsidy Removal on Standard of Living Amidst Rising Poverty in Nigeria. Asian Journal of Economics, Finance and Management, 5(1), 359–364. https://globalpresshub.com/index.php/AJEFM/article/view/1886
Yaziz, S. R., Ahmad, M. H., Nian, L. C., & Muhammad, N. (2011). A Comparative Study on Box-Jenkins and Garch Models in Forecasting Crude Oil Prices. Journal of Applied Sciences, 11(7), 1129–1135. https://doi.org/10.3923/jas.2011.1129.1135
Yi, A., Yang, M., & Li, Y. (2021). Macroeconomic Uncertainty and Crude Oil Futures Volatility - Evidence from China Crude Oil Futures Market. Frontiers in Environmental Science, 9, 1- 13. https://doi.org/10.3389/fenvs.2021.636903.
Yu, L., Wang, S., & Lai, K. K. (2008). Forecasting crude oil price with an EMD-based neural network ensemble learning paradigm. Energy Economics, 30(5), 2623–2635. https://doi.org/10.1016/j.eneco.2008.05.003
Marzo, M. & Zagaglia, P. (2010). Volatility forecasting for crude oil futures. Taylor & Francis Journals, 17(16), 1587-1599. https://doi.org/10.1080/13504850903084996
Zagaglia, M. M. &. P. (2010). Volatility forecasting for crude oil futures. ideas.repec.org. https://ideas.repec.org/a/taf/apeclt/v17y2010i16p1587-1599.html
Zhang, Y., Yao, T., He, L., & Ripple, R. (2019). Volatility forecasting of crude oil market: Can the regime switching GARCH model beat the single-regime GARCH models? International Review of Economics & Finance, 59(C), 302-317. https://doi.org/10.1016/j.iref.2018.09.006
Zolfaghari, M. and Gholami, S. (2021). A Hybrid Approach of Adaptive Wavelet Transform, Long Short-Term Memory and ARIMA-GARCH Family Models for the Stock Index Prediction. Expert Systems with Applications, 182(4), 115149. https://doi.org/10.1016/j.eswa.2021.115149
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Omorogbe Joseph Asemota, Mustapha Bello, Samuel Olorunfemi Adams
This work is licensed under a Creative Commons Attribution 4.0 International License.
