Abstract
Can we accurately predict the Brent oil price? If so, which forecasting method can provide the most accurate forecasts? To unravel these questions, we aim at predicting the weekly Brent oil price growth rate by using several forecasting methods that are based on different approaches. Basically, we assess and compare the out-of-sample performances of linear parametric models (the ARIMA, the ARFIMA and the autoregressive model), a nonlinear parametric model (the GARCH-in-Mean model) and different nonparametric data-driven methods (a nonlinear autoregressive artificial neural network, genetic programming and the nearest-neighbor method). The results obtained show that (1) all methods are capable of predicting accurately both the value and the directional change in the Brent oil price, (2) there are no significant forecasting differences among the methods and (3) the volatility of the series could be an important factor to enhance our predictive ability.
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Notes
The bootstrap confidence interval is constructed by using the accelerated bias-corrected (Bca) method, which has been demonstrated to perform better than other procedures under a wider variety of assumptions (Briggs et al. 1997). Moreover, it is recommended for general use (Efron and Tibshirani 1998). In our study, we also estimated confidence intervals by using different bootstrapping methods such as the normal approximation method, the percentile method, the percentile t-method and the bias-corrected percentile. The resulting empirical intervals were quite similar among them. For a more detailed explanation about the Bca bootstrap employed in our study, the reader is referred to Martínez and Martínez (2008).
The construction of the intervals through the surrogate method was done following the indications given in Álvarez-Díaz (2008). The autocorrelation values inside these intervals correspond to series that are assumed to be uncorrelated.
To save space, next subsection aims at providing a short explanation of the different forecasting methods used in our study. For a more detailed explanation, readers are referred to the references included in it.
Additionally, other parametric forecasting methods were included such as the recursive exponential smoothing method (Baumeister and Kilian 2012; Snudden 2018) and the backward-moving means (Snudden 2018). However, these methods showed a very poor performance. The forecasting assessment of an ARIMA estimated recursively was also taken into account, but there were not statistically differences with the ARIMA shown in this study. The forecasting results of these methods are not shown here, but they are available upon request.
In our study, we only show the results of the tricube weighted local regression. Other generalizations of the nearest-neighbor method were also considered (barycentric, unweighted local regression, exponential weighted local regression), but all of them performed worse than the tricube weighted local regression. The results of the others K-NN methods are available upon request.
As Chatfield (2000) affirms, researchers usually reserve about 10% of the data to make out-of-sample predictions. However, it must be said that this percentage has no theoretical background.
See, for example, Hyndman and Koehler (2006) for a description and definition of the different measures of forecasting assessment.
We also consider the mean absolute error (MAE) as metric to assess the forecasting performance of the methods. These results are not shown to save space, but they are available upon request.
We have also applied the test proposed by Harvey et al. (1997) that implies a small-sample modification of the Diebold–Mariano test. The values of the modified D–M test do not modify substantially the results reported in our study using the bootstrapped p values.
We have constructed more than five hundred neural networks by combining different number of lags, hidden units and activation functions. Moreover, we have also considered of the following transfer functions: linear, hyperbolic tangent sigmoid and log-sigmoid function. The NAR neural network that best fitted the data in the selection sample was characterized by the following architecture: The number of lags was 3 and the number of hidden units was also 3. The optimal design also implied a hyperbolic tangent sigmoid transfer specification for the activation functions and a linear form for the output function.
We follow the procedure recommended by Casdagli (1992) to select the optimal technical parameters of the K-NN. According to this procedure, the optimal number of lags and neighbors were 3 and 324, respectively.
See Giacomini and Rossi (2013) for a description of the most common tests used to compare the predictive ability of competing methods.
Complementary, the predictive comparisons were also made by using the D–M test. The results were qualitatively the same as those obtained by applying the G–W test. The pairwise comparison matrix according to the D–M test is available upon request.
References
Abdel-Aal RE (2008) Univariate modeling and forecasting of monthly energy demand time series using abductive and neural networks. Comput Ind Eng 54:903–917
Adrangi B, Chatrath A, Dhanda KK, Raffiee K (2001) Chaos in oil prices? Evidence from futures markets. Energy Econ 23:405–425
Alquist R, Kilian L, Vigfusson RJ (2013) Forecasting the price of oil. In: Elliot G, Timmermann A (eds) Handbook of economic forecasting, vol 2. Elsevier, Amsterdam, pp 427–507
Álvarez A, Orfila A, Tintoré J (2001) DARWIN- an evolutionary program for nonlinear modeling of chaotic time series. Comput Phys Commun 136:334–349
Álvarez-Díaz M (2008) Exchange rates forecasting: local or global methods? Appl Econ 40(15):1969–1984
Álvarez-Díaz M, Gupta R (2016) Forecasting the US consumer price index: does nonlinearity matter? Appl Econ 48(46):4462–4475
Bao Y, Zhang X, Yu L, Wang S (2007) Crude oil prediction based on multiscale decomposition. Lect Notes Comput Sci 4489:933–936
Bashiri-Behmiri N, Pires-Manso JR (2013) Crude oil price forecasting techniques: a comprehensive review of literature. Altern Invest Anal Rev 2(3):30–49
Baumeister C, Kilian L (2012) Real-time forecasts of the real price of oil. J Bus Econ Stat 30(2):326–336
Baumeister C, Kilian L (2014) What central bankers need to know about forecasting oil prices. Int Econ Rev 55(3):869–889
Binder KE, Pourahmadi M, Mjelde JW (2018) The role of temporal dependence in factor selection and forecasting oil prices. Empir Econ. https://doi.org/10.1007/s00181-018-1574-9
Bishop CM (1995) Neural networks for pattern recognition. Oxford University Press, Oxford
Briggs AH, Wonderling DE, Mooney CZ (1997) Pulling cost-effectiveness analysis up by its bootstraps: a non-parametric approach to confidence interval estimation. Health Econ 6:327–340
Casdagli M (1989) Non-linear prediction of chaotic time series. Physica D 35:35–356
Casdagli M (1992) Chaos and deterministic versus stochastic nonlinear modelling. J R Stat Soc Ser B (Stat Methodol) 54:303–328
Casdagli M, Eubank S, Farmer JD, Gibson J (1991) State space reconstruction in the presence of noise. Physica D 51:52–98
Chatfield C (2000) Time-series forecasting. Chapman & C Hall/CRC, New York
Cheong CW (2011) Parametric and non-parametric approaches in evaluating martingale hypothesis of energy spot market. Math Comput Model 54:1499–1509
Diebold FX (2013) Comparing predictive accuracy, twenty years later: a personal perspective on the use and abuse of Diebold–Mariano tests. Working Paper, University of Pennsylvania
Diebold FX (2015) Forecasting. Department of Economics, University of Pennsylvania. http://www.sas.upenn.edu/~fdiebold/Textbooks.html. Accessed 30 May 2016.
Diebold FX, Mariano RS (1995) Comparing predictive accuracy. J Bus Econ Stat 3:253–263
Efron B, Tibshirani RJ (1998) An introduction to the bootstrap. Chapman & Hall, Boca Raton
Farmer D, Siderowich J (1987) Predicting chaotic time series. Phys Rev Lett 59:845–848
Ferson W, Nallareddy S, Xie B (2013) The “out-of-sample” performance of long run risk models. J Financ Econ 107(3):537–556
Frey G, Manera M, Markandya A, Scarpa E (2009) Econometric models for oil price forecasting: a critical survey. In: CESifo Forum, vol 10. Institute for Economic Research at the University of Munich, pp 29–44 (2009)
Gençay R (1999) Linear, non-linear and essential foreign exchange rate prediction with simple technical trading rule. J Int Econ 47:91–107
Ghaffari A, Zare S (2009) A novel algorithm for prediction of crude oil price variation based on soft computing. Energy Econ 31(4):531–536
Giacomini R, Rossi B (2013) Forecasting in Macroeconomics. In: Hashimzade N, Thornton MA (eds) Handbook of research methods and applications in empirical macroeconomics. Edward Elgar Publishing, Massachusetts
Giacomini R, White H (2006) Tests of conditional predictive ability. Econometrica 74:1545–1578
Harvey DI, Leybourne SJ, Newbold P (1997) Testing the equality of prediction mean squared errors. Int J Forecast 13:281–291
He K, Yu L, Lai KK (2012) Crude oil price analysis and forecasting using wavelet decomposed ensemble model. Energy 46:64–574
Hsieh DA (1991) Chaos and nonlinear dynamics: applications to financial markets. J Finance 46:1839–1877
Huntington H (1994) Oil price forecasting in the 1980s: what went wrong? Energy Journal 15:1–22
Hyndman RJ, Koehler AB (2006) Another look at measures of forecast accuracy. Int J Forecast 22:679–688
Jaditz T, Riddick LA (2000) Time-series near-neighbor regression. Stud Nonlinear Dyn Econom 4(1):35–44
Jammazi R, Aloui C (2012) Crude oil price forecasting: experimental evidence from wavelet decomposition and neural network modeling. Energy Econ 34:828–841
Kaastra I, Boyd M (1996) Designing a neural network for forecasting financial and economic time series. Neurocomputing 10:215–236
Kaboudan MA (2001) Compumetric forecasting of crude oil prices. In: Proceedings of the 2001 congress on evolutionary computation, vol 1, pp 283–287
Khazem H, Mazouz A (2013) Forecasting the price of crude oil using artificial neural networks. Int J Bus Mark Decis Sci 6(1):119–135
Koza JR (1992) Genetic programming: On the programming of computers by means of natural selection. The MIT Press, Cambridge
Liu L, Wang Y, Yang L (2018) Predictability of crude oil prices: an investor perspective. Energy Econ 75:193–205
Longo C, Manera M, Markandya A (2007) Evaluating the empirical performance of alternative economic models for oil price forecasting. Technical Report 4.2007, Fondazione Eni Enrico Mattei
Martínez W, Martínez AR (2008) Computational statistics handbook with MATLAB. Chapman & Hall/CRC, Boca Raton
Mohammadi H, Su L (2010) International evidence on crude oil price dynamics: applications of ARIMA-GARCH models. Energy Econ 32:1001–1008
Morana C (2001) A semiparametric approach to short-term oil price forecasting. Energy Econ 23(3):325–338
Moshiri S, Foroutan F (2006) Forecasting nonlinear crude oil futures prices. Energy J 27(4):81–96
Panas E, Ninni V (2000) Are oil markets chaotic? A non-linear dynamic analysis. Energy Econ 22(5):549–568
Pesaran MH, Timmermann A (1992) A simple nonparametric test of predictive performance. J Bus Econ Stat 10(4):461–465
Pindyck RS (1999) The long-run evolution of energy prices. Energy J 20:1–27
Sehgal N, Pandey KK (2015) Artificial intelligence methods for oil price forecasting: a review and evaluation. Energy Syst 4:479–506
Shabri A, Samsudin R (2014) Daily crude oil price forecasting using hybridizing wavelet and artificial neural network model. Math Probl Eng 1–10, article ID 201402
Shen S, Li G, Song H (2008) An assessment of combining tourism demand forecasts over different time horizons. J Travel Res 47:197
Snudden S (2018) Targeted growth rates for long-horizon crude oil price forecasts. Int J Forecast 34(1):1–16
Takens F (1981) Detecting strange attractors in turbulence. In: Rand DA, Young LS (eds) Dynamical systems and turbulence. Springer, Berlin
Tularam GA, Saeed T (2016) Oil-price forecasting based on various univariate time-series models. Am J Oper Res 6:226–235
Wang J, Li X (2018) A combined neural network model for commodity price forecasting with SSA. Soft Comput 22:5323–5533
Wei Y, Wang Y, Huang D (2010) Forecasting crude oil market volatility: further evidence using GARCH class models. Energy Econ 32(6):1477–1484
Weigend AS, Gershenfeld NA (1993) Time series prediction: forecasting the future and understanding the past. Addison-Wesley, Reading
Xie W, Yu L, Xu SY, Wang SY (2006) A new method for crude oil price forecasting based on support vector machines. Lect Notes Comput Sci 3994:441–451
Yadavalli VK, Dahule RK, Tambe SS, Kulkarni BD (1999) Obtaining functional form for chaotic time series evolution using genetic algorithm. Am Inst Phys 9(3):789–794
Yao J, Tan CL (2000) A case study on using neural networks to perform technical forecasting of Forex. Neurocomputing 34:79–98
Yu L, Wang S, Lai KK (2008) Forecasting crude oil price with an EMD-based neural network ensemble learning paradigm. Energy Econ 30:2623–2635
Zhang GP (2007) Avoiding pitfalls in neural network research. IEEE Trans Syst Man Cybernet Part C Appl Rev 37(1):3–16
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Álvarez-Díaz, M. Is it possible to accurately forecast the evolution of Brent crude oil prices? An answer based on parametric and nonparametric forecasting methods. Empir Econ 59, 1285–1305 (2020). https://doi.org/10.1007/s00181-019-01665-w
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DOI: https://doi.org/10.1007/s00181-019-01665-w