Time-series-based forecasting is essential to determine how past events affect future events. This paper compares the performance accuracy of different time-series models for oil prices. Three types of univariate models are discussed: the exponential smoothing (ES), Holt-Winters (HW) and autoregressive intergrade moving average (ARIMA) models. To determine the best model, six different strategies were applied as selection criteria to quantify these models’ prediction accuracies. This comparison should help policy makers and industry marketing strategists select the best forecasting method in oil market. The three models were compared by applying them to the time series of regular oil prices for West Texas Intermediate (WTI) crude. The comparison indicated that the HW model performed better than the ES model for a prediction with a confidence interval of 95%. However, the ARIMA (2, 1, 2) model yielded the best results, leading us to conclude that this sophisticated and robust model outperformed other simple yet flexible models in oil market.
KeywordsOil PriceUnivariate Time SeriesExponential SmoothingHolt-WintersARIMA ModelsModel Selection Criteria
Tsay, R.S. (2000) Time Series and Forecasting: Brief History and Future Research. Journal of the American Statistical Association, 95, 638-643. http://dx.doi.org/10.1080/01621459.2000.10474241
Hetemaki, L. and Mikkola, J. (2005) Forecasting Germany’s Printing and Writing Paper Imports. Forest Science,.51, 483-497.
Peralta, J., Li, X.D., Gutierrez, G. and Sanchis, A. (2010) Time Series Forecasting by Evolving Artificial Neural Networks Using Genetic Algorithms and Differential Evolution. The 2010 International Joint Conference on Neural Networks, Barcelona, 18-23 July 2010, 1-8.
Makridakis, S., Wheelwright, S.C. and Hyndman, R.J. (1998) Forecasting: Methods and Applications. 3rd Edition, Wiley, Hoboken.
Wang, X., Guo, P. and Huang, X. (2011) A Review of Wind Power Forecasting Models. Energy Procedia, 12, 770- 778. http://dx.doi.org/10.1016/j.egypro.2011.10.103
Xiong, T., Bao, Y. and Hu, Z. (2013) Beyond One-Step-Ahead Forecasting: Evaluation of Alternative Multi-Step- Ahead Forecasting Models for Crude Oil Prices. Energy Economics, 40, 405-415. http://dx.doi.org/10.1016/j.eneco.2013.07.028
Diebold, F.X. and Mariano, R.S. (2002) Comparing Predictive Accuracy. Journal of Business & Economic Statistics, 20, 134-144. http://dx.doi.org/10.1198/073500102753410444
Bermúdez, J., Segura, J. and Vercher, E. (2006) Improving Demand Forecasting Accuracy Using Nonlinear Programming Software. Journal of the Operational Research Society, 57, 94-100. http://dx.doi.org/10.1057/palgrave.jors.2601941
Wang, X., Smith-Miles, K. and Hyndman, R. (2009) Rule Induction for Forecasting Method Selection: Meta-Learning the Characteristics of Univariate Time Series. Neurocomputing, 72, 2581-2594. http://dx.doi.org/10.1016/j.neucom.2008.10.017
Poskitt, D.S. (2003) On the Specification of Cointegrated Autoregressive Moving-Average Forecasting Systems. International Journal of Forecasting, 19, 503-519. http://dx.doi.org/10.1016/S0169-2070(02)00031-6
Herrera, A.M. and Pesavento, E. (2009) Oil Price Shocks, Systematic Monetary Policy, and the “Great Moderation”. Macroeconomic Dynamics, 13, 107-137. http://dx.doi.org/10.1017/S1365100508070454
Abdel-Aal, R.E. (2008) Univariate Modeling and Forecasting of Monthly Energy Demand Time Series Using Abductive and Neural Networks. Computers & Industrial Engineering, 54, 903-917. http://dx.doi.org/10.1016/j.cie.2007.10.020
Tavakkoli, A., Hemmasi, A.H., Talaeipour, M., Bazyar, B. and Tajdini, A. (2015) Forecasting of Particleboard Consumption in Iran Using Univariate Time Series Models. BioResources, 10, 2032-2043. http://ojs.cnr.ncsu.edu/index.php/BioRes/article/view/BioRes_10_2_2032_Tavakkoli_Forecasting_Particleboard_Consumption
Broze, L. and Mélard, G. (1990) Exponential Smoothing: Estimation by Maximum Likelihood. Journal of Forecasting, 9, 445-455. http://dx.doi.org/10.1002/for.3980090504
Makridakis, S. and Hibon, M. (2000) The M3-Competition: Results, Conclusions and Implications. International Journal of Forecasting, 16, 451-476. http://dx.doi.org/10.1016/S0169-2070(00)00057-1
George, E.P.B., Jenkins, G.M. and Reinsel, G.C. (2008) Time Series Analysis: Forecasting and Control. 4th Edition, Wiley, Hoboken.
Hyndman, R., Koehler, A., Ord, K. and Snyder, R. (2008) Forecasting with Exponential Smoothing: The State Space Approach. Springer Science and Business Media, Berlin. http://dx.doi.org/10.1007/978-3-540-71918-2
Gardner Jr., E.S. (2006) Exponential Smoothing: The State of the Art—Part II. International Journal of Forecasting, 22, 637-666. http://dx.doi.org/10.1016/j.ijforecast.2006.03.005
Chatfield, C. and Yar, M. (1988) Holt-Winters Forecasting: Some Practical Issues. Journal of the Royal Statistical Society. Series D (The Statistician), 37, 129-140. http://dx.doi.org/10.2307/2348687
Gelper, S., Fried, R. and Croux, C. (2010) Robust Forecasting with Exponential and Holt-Winters Smoothing. Journal of Forecasting, 29, 285-300.
Zhang, G.P. (2003) Time Series Forecasting Using a Hybrid ARIMA and Neural Network Model. Neurocomputing, 50, 159-175. http://dx.doi.org/10.1016/S0925-2312(01)00702-0
Assis, K., Amran, A. and Remali, Y. (2006) Forecasting Cocoa Bean Prices Using Univariate Time Series Models. Journal of Arts, Science and Commerce, 1, 2229-4686. http://www.researchersworld.com/vol1/Paper_7.pdf
Gahirwal, M. (2013) Inter Time Series Sales Forecasting. arXiv:1303.0117
Chatfield, C. (2000) Time-Series Forecasting. CRC Press, Boca Raton. http://dx.doi.org/10.1201/9781420036206
McKenzie, E. (1984) General Exponential Smoothing and the Equivalent Arma Process. Journal of Forecasting, 3, 333-344. http://dx.doi.org/10.1002/for.3980030312
Newaz, M.K. (2008) Comparing the Performance of Time Series Models for Forecasting Exchange Rate. BRAC University Journal, 5, 55-65.
Ahmad, W. and Ahmad, S. (2013) Arima Model and Exponential Smoothing Method: A Comparison. AIP Conference Proceedings, 1522, 1312-1321. http://dx.doi.org/10.1063/1.4801282
Burger, C., Dohnal, M., Kathrada, M. and Law, R. (2001) A Practitioners Guide to Time-Series Methods for Tourism Demand Forecasting—A Case Study of Durban, South Africa. Tourism Management, 22, 403-409. http://dx.doi.org/10.1016/S0261-5177(00)00068-6
Madden, G. and Tan, J. (2007) Forecasting Telecommunications Data with Linear Models. Telecommunications Policy, 31, 31-44. http://dx.doi.org/10.1016/j.telpol.2006.11.004
Da Veiga, C.P., Da Veiga, C.R.P., Catapan, A., Tortato, U. and Da Silva, W.V. (2014) Demand Forecasting in Food Retail: A Comparison between the Holt-Winters and ARIMA Models. WSEAS Transactions on Business and Economics, 11, 608-614.
Udom, P. and Phumchusri, N. (2014) A Comparison Study between Time Series Model and ARIMA Model for Sales Forecasting of Distributor in Plastic Industry. IOSR Journal of Engineering, 4, 32-38. http://dx.doi.org/10.9790/3021-04213238
Lim, C. and McAleer, M. (2001) Forecasting Tourist Arrivals. Annals of Tourism Research, 28, 965-977. http://dx.doi.org/10.1016/S0160-7383(01)00006-8
Nazim, A. and Afthanorhan, A. (2014) A Comparison between Single Exponential Smoothing (SES), Double Exponential Smoothing (DES), Holts (Brown) and Adaptive Response Rate Exponential Smoothing (ARRES) Techniques in Forecasting Malaysia Population. Global Journal of Mathematical Analysis, 2, 276-280. http://dx.doi.org/10.14419/gjma.v2i4.3253
Wilmot, N.A. (2013) Cointegration in the Oil Market among Regional Blends. International Journal of Energy Economics and Policy, 3, 424-433.
Tularam, G.A. (2010) Relationship between El Nino Southern Oscillation Index and Rainfall (Queensland, Australia). International Journal of Sustainable Development and Planning, 5, 378-391. http://dx.doi.org/10.2495/SDP-V5-N4-378-391
Ord, J.K., Koehler, A.B. and Snyder, R.D. (1997) Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models. Journal of the American Statistical Association, 92, 1621-1629. http://dx.doi.org/10.1080/01621459.1997.10473684
Billah, B., King, M.L., Snyder, R.D. and Koehler, A.B. (2006) Exponential Smoothing Model Selection for Forecasting. International Journal of Forecasting, 22, 239-247. http://dx.doi.org/10.1016/j.ijforecast.2005.08.002
Ramanathan, R. (2002) Introductory Econometrics with Applications. 5th Edition, Thomson Learning, Stamford, 688.
Goodwin, P. and Lawton, R. (1999) On the Asymmetry of the Symmetric MAPE. International Journal of Forecasting, 15, 405-408. http://dx.doi.org/10.1016/S0169-2070(99)00007-2