Abstract
An accurate forecasting model for the price volatility of minerals plays a vital role in future investments and decisions for mining projects and related companies. In this paper, a hybrid model is proposed to provide an accurate model for forecasting the volatility of copper prices. The proposed model combines the adaptive neuro-fuzzy inference system (ANFIS) and genetic algorithm (GA). Genetic algorithms are used for estimating the ANFIS model parameters. The results of the proposed model are compared to other models, including ANFIS, support vector machine (SVM), generalized autoregressive conditional heteroscedasticity (GARCH), and autoregressive integrated moving average (ARIMA) models. The empirical results confirm the superiority of the hybrid GA–ANFIS model over other models. The proposed model also improves the forecasting accuracy obtained from the ANFIS, SVM, GARCH, and ARIMA models by a 62.92%, 36.38%, 91.72%, and 42.19% decrease in mean square error, respectively.
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Abdel Sabour, S. A., & Poulin, R. (2006). Valuing real capital investments using the least-squares Monte Carlo method. The Engineering Economist, 51(2), 141–160. https://doi.org/10.1080/00137910600705210.
Aminrostamkolaee, B., Scroggs, J. S., Borghei, M. S., Safdari-Vaighani, A., Mohammadi, T., & Pourkazemi, M. H. (2017). Valuation of a hypothetical mining project under commodity price and exchange rate uncertainties by using numerical methods. Resources Policy, 52, 296–307. https://doi.org/10.1016/j.resourpol.2017.04.004.
Aminul Haque, M., Topal, E., & Lilford, E. (2016). Estimation of mining project values through real option valuation using a combination of hedging strategy and a mean reversion commodity price. Natural Resources Research, 25(4), 459–471. https://doi.org/10.1007/s11053-016-9294-3.
Angus, A., Casado, M. R., & Fitzsimons, D. (2012). Exploring the usefulness of a simple linear regression model for understanding price movements of selected recycled materials in the UK. Resources, Conservation and Recycling, 60, 10–19. https://doi.org/10.1016/j.resconrec.2011.10.011.
Atsalakis, G. (2014). New technology product demand forecasting using a fuzzy inference system. Operational Research, 14(2), 225–236. https://doi.org/10.1007/s12351-014-0160-y.
Atsalakis, G. S. (2016). Using computational intelligence to forecast carbon prices. Applied Soft Computing, 43, 107–116. https://doi.org/10.1016/j.asoc.2016.02.029.
Atsalakis, G., Frantzis, D., & Zopounidis, C. (2016a). Commodities price trend forecasting by a neuro-fuzzy controller. Energy Systems, 7(1), 73–102. https://doi.org/10.1007/s12667-015-0154-8.
Atsalakis, G. S., Protopapadakis, E. E., & Valavanis, K. P. (2016b). Stock trend forecasting in turbulent market periods using neuro-fuzzy systems. Operational Research, 16(2), 245–269. https://doi.org/10.1007/s12351-015-0197-6.
Behmiri, N. B., & Manera, M. (2015). The role of outliers and oil price shocks on volatility of metal prices. Resources Policy, 46, 139–150. https://doi.org/10.1016/j.resourpol.2015.09.004.
Bodart, V., Candelon, B., & Carpantier, J.-F. (2015). Real exchanges rates, commodity prices and structural factors in developing countries. Journal of International Money and Finance, 51, 264–284. https://doi.org/10.1016/j.jimonfin.2014.11.021.
Buncic, D., & Moretto, C. (2015). Forecasting copper prices with dynamic averaging and selection models. The North American Journal of Economics and Finance, 33, 1–38. https://doi.org/10.1016/j.najef.2015.03.002.
Buyuksahin, B., & Robe, M. A. (2014). Speculators, commodities and cross-market linkages. Journal of International Money and Finance, 42, 38–70. https://doi.org/10.1016/j.jimonfin.2013.08.004.
Chatterjee, S., Sethi, M. R., & Asad, M. W. A. (2016). Production phase and ultimate pit limit design under commodity price uncertainty. European Journal of Operational Research, 248(2), 658–667. https://doi.org/10.1016/j.ejor.2015.07.012.
Chen, Y., He, K., & Zhang, C. (2016). A novel grey wave forecasting method for predicting metal prices. Resources Policy, 49, 323–331. https://doi.org/10.1016/j.resourpol.2016.06.012.
Chen, Y. C., Rogoff, K. S., & Rossi, B. (2010). Can exchange rates forecast commodity prices? The Quarterly Journal of Economics, 125(3), 1145–1194.
Ciner, C. (2017). Predicting white metal prices by a commodity sensitive exchange rate. International Review of Financial Analysis, 52, 309–315. https://doi.org/10.1016/j.irfa.2017.04.002.
Cologni, A., & Manera, M. (2008). Oil prices, inflation and interest rates in a structural cointegrated VAR model for the G-7 countries. Energy Economics, 30(3), 856–888. https://doi.org/10.2139/ssrn.843505.
Di Pillo, G., Latorre, V., Lucidi, S., & Procacci, E. (2016). An application of support vector machines to sales forecasting under promotions. 4OR, 14(3), 309–325. https://doi.org/10.1007/s10288-016-0316-0.
Dooley, G., & Lenihan, H. (2005). An assessment of time series methods in metal price forecasting. Resources Policy, 30(3), 208–217. https://doi.org/10.1016/j.resourpol.2005.08.007.
Dubey, A. D., & IEEE (2016). Gold Price Prediction using Support Vector Regression and ANFIS models. In 2016 International Conference on Computer Communication and Informatics (International Conference on Computer Communication and Informatics).
Ediger, V. Ş., & Akar, S. (2007). ARIMA forecasting of primary energy demand by fuel in Turkey. Energy Policy, 35(3), 1701–1708. https://doi.org/10.1016/j.enpol.2006.05.009.
Fritz, M., & Berger, P. D. (2015). Chapter 3—Comparing two designs (or anything else!) using paired sample t tests. In M. Fritz & P. D. Berger (Eds.), Improving the user experience through practical data analytics (pp. 71–89). Boston: Morgan Kaufmann.
García, D., & Kristjanpoller, W. (2019). An adaptive forecasting approach for copper price volatility through hybrid and non-hybrid models. Applied Soft Computing, 74, 466–478. https://doi.org/10.1016/j.asoc.2018.10.007.
Goldberg, D. E., & Holland, J. H. (1988). Genetic algorithms and machine learning. Machine Learning, 3(2), 95–99.
Han, F., Yu, F., & Cui, Z. (2016). Industrial metabolism of copper and sulfur in a copper-specific eco-industrial park in China. Journal of Cleaner Production, 133, 459–466. https://doi.org/10.1016/j.jclepro.2016.05.184.
Haque, M. A., Topal, E., & Lilford, E. (2015). Relationship between the Gold Price and the Australian Dollar—US Dollar Exchange Rate. Mineral Economics, 28, 65–78. https://doi.org/10.1007/s13563-015-0067-y.
He, Y., Wang, S., & Lai, K. K. (2010). Global economic activity and crude oil prices: A cointegration analysis. Energy Economics, 32(4), 868–876. https://doi.org/10.1016/j.eneco.2009.12.005.
Hernández, E. (2017). Volatility of main metals forecasted by a hybrid ANN–GARCH model with regressors. Expert Systems with Applications, 84, 290–300. https://doi.org/10.1016/j.eswa.2017.05.024.
Ho, R. (2006). Handbook of univariate and multivariate data analysis and interpretation with SPSS. Boca Raton: Chapman & Hall/CRC.
Huang, C., Davis, L., & Townshend, J. (2002). An assessment of support vector machines for land cover classification. International Journal of Remote Sensing, 23(4), 725–749. https://doi.org/10.1080/01431160110040323.
Jang, J.-S. (1993). ANFIS: adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man, and Cybernetics, 23(3), 665–685.
Khashei, M., & Bijari, M. (2010). An artificial neural network (p, d, q) model for time series forecasting. Expert Systems with Applications, 37(1), 479–489. https://doi.org/10.1016/j.eswa.2009.05.044.
Khashei, M., & Bijari, M. (2011). A novel hybridization of artificial neural networks and ARIMA models for time series forecasting. Applied Soft Computing, 11(2), 2664–2675. https://doi.org/10.1016/j.asoc.2010.10.015.
Kiani Mavi, R., Kiani Mavi, N., & Goh, M. (2017). Modeling corporate entrepreneurship success with ANFIS. Operational Research, 17(1), 213–238. https://doi.org/10.1007/s12351-015-0223-8.
Kriechbaumer, T., Angus, A., Parsons, D., & Casado, M. R. (2014). An improved wavelet–ARIMA approach for forecasting metal prices. Resources Policy, 39, 32–41. https://doi.org/10.1016/j.resourpol.2013.10.005.
Kristjanpoller, W., & Minutolo, M. C. (2015). Gold price volatility: A forecasting approach using the Artificial Neural Network–GARCH model. Expert Systems with Applications, 42(20), 7245–7251. https://doi.org/10.1016/j.eswa.2015.04.058.
Kristjanpoller, W., & Minutolo, M. C. (2016). Forecasting volatility of oil price using an artificial neural network–GARCH model. Expert Systems with Applications, 65, 233–241. https://doi.org/10.1016/j.eswa.2016.08.045.
Lardic, S., & Mignon, V. (2008). Oil prices and economic activity: An asymmetric cointegration approach. Energy Economics, 30(3), 847–855. https://doi.org/10.1016/j.eneco.2006.10.010.
Larson, R., & Farber, B. (2010). Elementary statistics: Picturing the world (4th ed.). London: Pearson.
Lasheras, F. S., de Cos Juez, F. J., Sánchez, A. S., Krzemień, A., & Fernández, P. R. (2015). Forecasting the COMEX copper spot price by means of neural networks and ARIMA models. Resources Policy, 45, 37–43. https://doi.org/10.1016/j.resourpol.2015.03.004.
Li, L., Pan, D., Li, B., Wu, Y., Wang, H., Gu, Y., et al. (2017). Patterns and challenges in the copper industry in China. Resources, Conservation and Recycling, 127, 1–7. https://doi.org/10.1016/j.resconrec.2017.07.046.
Lineesh, M., Minu, K., & John, C. J. Analysis of nonstationary nonlinear economic time series of gold price: A comparative study. In International mathematical forum, 2010 (Vol. 5, pp. 1673–1683, Vol. 34).
Liu, C., Hu, Z., Li, Y., & Liu, S. (2017). Forecasting copper prices by decision tree learning. Resources Policy, 52, 427–434. https://doi.org/10.1016/j.resourpol.2017.05.007.
Liu, C., Liu, Q., Li, J., Li, Y., & Wang, A. (2018). China’s Belt and road initiative in support of the resourcing future generations program. Natural Resources Research, 27(2), 257–274. https://doi.org/10.1007/s11053-017-9342-7.
Mitchell, M. (1998). An introduction to genetic algorithms. Bradford: Bradford Books.
Molugaram, K., & Rao, G. S. (2017). Chapter 6 - Correlation and Regression. In K. Molugaram & G. S. Rao (Eds.), Statistical techniques for transportation engineering (pp. 293–329). Oxford: Butterworth-Heinemann.
Orlowski, L. T. (2017). Volatility of commodity futures prices and market-implied inflation expectations. Journal of International Financial Markets, Institutions and Money, 51, 133–141. https://doi.org/10.1016/j.intfin.2017.10.002.
Paithankar, A., & Chatterjee, S. (2017). Grade and tonnage uncertainty analysis of an african copper deposit using multiple-point geostatistics and sequential Gaussian simulation. Natural Resources Research. https://doi.org/10.1007/s11053-017-9364-1.
Panigrahi, B. K., Suganthan, P. N., Das, S., & Dash, S. S. (2013). Swarm, evolutionary, and memetic computing: 4th international conference, SEMCCO 2013, Chennai, India, December 19–21, 2013, proceedings (Vol. pt. 2). Berlin: Springer.
Parisi, A., Parisi, F., & Díaz, D. (2008). Forecasting gold price changes: Rolling and recursive neural network models. Journal of Multinational Financial Management, 18(5), 477–487. https://doi.org/10.1016/j.mulfin.2007.12.002.
Sauvageau, M., & Kumral, M. (2017). Kalman filtering-based approach for project valuation of an iron ore mining project through spot price and long-term commitment contracts. Natural Resources Research, 26(3), 303–317. https://doi.org/10.1007/s11053-017-9329-4.
Shafiee, S., & Topal, E. (2010). An overview of global gold market and gold price forecasting. Resources Policy, 35(3), 178–189. https://doi.org/10.1016/j.resourpol.2010.05.004.
Sung, A. H., & Mukkamala, S. Identifying important features for intrusion detection using support vector machines and neural networks. In 2003 symposium on applications and the internet, 2003. Proceedings, 2003 (pp. 209–216). Washington: IEEE.
Vapnik, A. C. (1974). Nauka. USSR.
Wang, M., Chen, W., Zhou, Y., & Li, X. (2017). Assessment of potential copper scrap in China and policy recommendation. Resources Policy, 52, 235–244. https://doi.org/10.1016/j.resourpol.2016.12.009.
Wang, T., & Wang, C. (2017). The spillover effects of China’s industrial growth on price changes of base metal. Resources Policy. https://doi.org/10.1016/j.resourpol.2017.11.007.
Wang, C., Zuo, L., Hu, P., Yao, H., & Hao, Z. (2013). Evaluation and simulation analysis of China’s copper security evolution trajectory. Transactions of Nonferrous Metals Society of China, 23(8), 2465–2474. https://doi.org/10.1016/S1003-6326(13)62756-9.
Wen, F. H., Yang, X., Gong, X., & Lai, K. K. (2017). Multi-scale volatility feature analysis and prediction of gold price. International Journal of Information Technology & Decision Making, 16(1), 205–223. https://doi.org/10.1142/s0219622016500504.
Wets, R. J., & Rios, I. (2015). Modeling and estimating commodity prices: Copper prices. Mathematics and Financial Economics, 9(4), 247–270. https://doi.org/10.1007/s11579-014-0140-2.
Whitley, D. (1994). A genetic algorithm tutorial. Statistics and Computing, 4(2), 65–85.
Yaghoobi, A., Bakhshi-Jooybari, M., Gorji, A., & Baseri, H. (2016). Application of adaptive neuro fuzzy inference system and genetic algorithm for pressure path optimization in sheet hydroforming process. The International Journal of Advanced Manufacturing Technology, 86(9–12), 2667–2677. https://doi.org/10.1007/s00170-016-8349-2.
Yazdani-Chamzini, A., Yakhchali, S. H., Volungevičienė, D., & Zavadskas, E. K. (2012). Forecasting gold price changes by using adaptive network fuzzy inference system. Journal of Business Economics and Management, 13(5), 994–1010. https://doi.org/10.3846/16111699.2012.683808.
Yu, M. (2009). Revaluation of the Chinese Yuan and triad trade: A gravity assessment. Journal of Asian Economics., 20(6), 655–668. https://doi.org/10.1016/j.asieco.2009.09.008.
Zhang, G. P. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159–175. https://doi.org/10.1016/S0925-2312(01)00702-0.
Zhang, L., Chen, T., Yang, J., Cai, Z., Sheng, H., Yuan, Z., et al. (2017). Characterizing copper flows in international trade of China, 1975–2015. Science of the Total Environment, 601, 1238–1246. https://doi.org/10.1016/j.scitotenv.2017.05.216.
Zhang, C., & Tu, X. (2016). The effect of global oil price shocks on China’s metal markets. Energy Policy, 90, 131–139. https://doi.org/10.1016/j.enpol.2015.12.012.
Zhang, L., Yang, J., Cai, Z., & Yuan, Z. (2014). Analysis of copper flows in China from 1975 to 2010. Science of the Total Environment, 478, 80–89. https://doi.org/10.1016/j.scitotenv.2014.01.070.
Zheng, Y., Shao, Y., & Wang, S. (2017). The determinants of Chinese nonferrous metals imports and exports. Resources Policy, 53(1), 238–246. https://doi.org/10.1016/j.resourpol.2017.06.003.
Zou, H. F., Xia, G. P., Yang, F. T., & Wang, H. Y. (2007). An investigation and comparison of artificial neural network and time series models for Chinese food grain price forecasting. Neurocomputing, 70(16), 2913–2923. https://doi.org/10.1016/j.neucom.2007.01.009.
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This work was supported by Chinese Guizhou Science and Technology Planning Project (20172803) and Chinese Hubei Natural Science Foundation (2016CFB336). Zakaria Alameer appreciates the financial support from the Chinese Scholarship Council (CSC) and the Egyptian Government.
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Alameer, Z., Elaziz, M.A., Ewees, A.A. et al. Forecasting Copper Prices Using Hybrid Adaptive Neuro-Fuzzy Inference System and Genetic Algorithms. Nat Resour Res 28, 1385–1401 (2019). https://doi.org/10.1007/s11053-019-09473-w
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DOI: https://doi.org/10.1007/s11053-019-09473-w