Oil price data are available at a high frequency and therefore, there is increasing evidence of the presence of statistically significant correlations between observations that are large apart and possibility of conditional heteroskedasticity. This paper empirically analyzes the crude oil price return volatility patterns using autoregressive integrated moving average (ARIMA) and generalized autoregressive conditional heteroskedasticity (GARCH) family models. The results reveal that GARCH (1, 1) and ARIMA (1, 1, 0) models perform well in capturing the stylistic features present in high frequency crude oil prices in Nigeria within the sampled period. The Holt-Winters forecast made for twenty six (26) months using ARIMA (1, 1, 0) was approximately close to the real price of crude oil per barrel as evident from the 95% confidence interval estimates. The paper practically disseminates independent and impartial crude oil price information to promote sound policymaking, efficient markets and understanding of crude oil price and its interaction with the economy and the environment.
symmetric, forecast, ARIMA models, volatility clustering
 Akaike H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control AC-19: 716-723.
 Bartlett MS. (1946). On the theoretical specification of sampling properties of autocorrelated time series. Journal of the Royal Statistical Society B 8: 27-41. https://doi.org/10.2307/2983611
 Bollerslev T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometric 31: 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
 Box GEP, Jenkins GM. (1976). Time series analysis: Forecasting and control. revised edition, San Francisco: Holden Day. https://doi.org/10.1111/j.1467-9892.2009.00643.x
 Central Bank of Nigeria (CBN). (2009). Annual Reports and statement of Accounts for the year ended 31st December.
 Contreras J, Espinola R, Nogales FJ, Conejo AJ. (2003). ARIMA models to predict next day electricity prices. IFEE Transactions on Power System 18(3): 1014-1020. https://doi.org/10.1109/MPER.2002.4312577
 Dickey DA, Fuller WA. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74: 427-31. https://doi.org/10.1109/MPER.2002.4312577
 Engle, Robert F. (1982). Autoregressive conditional heteroscedasticity with estimates of variance of United Kingdom Inflation. Econometric 50: 987-1008. https://doi.org/10.2307/1912773
 Energy Information Administration (EIA) (2004). U.S. Primary Energy Consumption by Source and Sector.
 Gabralla LA, Abraham A. (2013). Computational modeling of crude oil price forecasting: A review of two decade of research. International Journal of Computer Information System and Industrial Management Applications 5: 729-740.
 Imam RO. (2017). ARIMA model for forecasting crude oil prices in Nigeria. An M.Sc. Project, Department of Mathematics, University of Lagos, Nigeria.
 Kwiatkowski D, Phillips CBP, Schmidt P, Shin Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics 54: 159-178.
 Ljung GM, Box GEP. (1978). On a measure of lack of fit in time series models. Biometrika 65: 297-303. https://doi.org/10.2307/2335207
 Mandelbrot B. (1963). The variation of certain speculative prices. Journal of Business 36: 394-419. https://doi.org/10.1007/978-1-4757-2763-0_14
 Onyeka-Ubaka JN. (2013). A modifield BL-GARCH for distributions with heavy tails. A Ph.D. Thesis, Department of Mathematics, University of Lagos, Nigeria.
 Onyeka-Ubaka JN, Abass O. (2013). Central Bank of Nigeria (CBN) intervention and the future of stocks in the banking sector. American Journal of Mathematics and Statistics 3(6): 407-416.
 Onyeka-Ubaka JN, Abass O, Okafor RO. (2014). Conditional variance parameters in symmetric models. International Journal of Probability and Statistics 3(1): 1-7. https://doi.org/10.5923/j.ijps.20140301.01
 Onyeka-Ubaka JN, Abass O, Okafor RO. (2016). A generalized t-distribution based filter for stochastic volatility models. AMSE JournalS-2016-Series: Advances D 21(1): 19-37.
 Poon S, Grander C. (2005). Practical issues in forecasting volatility. Financial Analysis Journal 61(1): 45-56. https://doi.org/10.2469/faj.v61.n1.2683
 Schwert GW. (1989). Why does stock market volatility change over time? Journal of Finance 44: 1115-1153. https://doi.org/10.2307/2328636
 Zhu F. (2011). A negative binomial integer-valued GARCH model. Journal of Time Series Analysis 32: 54-67. https://doi.org/10.1111/j.1467-9892.2010.00684