Abstract
Copper is one of the main non-ferrous metals which are closely associated with important industries, such as equipment manufacturing, electrical wiring, and construction; and thus, copper price is becoming an important impact factor on the performance of related economies. This paper aims to develop a hybrid method for forecasting the copper price by combining empirical wavelet transform (EWT), particle swarm optimization (PSO), gravitational search algorithm (GSA) and long short term memory neural network (LSTM), which is denoted as EWT-PSO-GSA-LSTM in this study. The forecasting performance of the proposed hybrid method was verified by time series data of the copper closing price in the London Metal Exchange (LME). The results of this study have shown that the proposed EWT-PSO-GSA-LSTM method outperformed other forecasting methods in terms of several performance criteria, such as the root mean square error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE), and the Diebold–Mariano (DM) test. For the daily copper price time series, the EWT-PSO-GSA-LSTM method had the smallest RMSE, MAE and MAPE values (0.007, 0.013 and 1.358, respectively) compared to LSTM, EWT-LSTM, PSO-LSTM and EWT-PSO-LSTM methods. Furthermore, all the DM values of our proposed method were below -2.61 and the \(p\) values were smaller than 1%, indicating that the proposed method performed the best in forecasting the copper price at the 99% confidence level. Given the present results, it can be concluded that it is possible to improve the copper price forecasting method by combining the EWT, PSO, GSA and LSTM models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Code availability
Not applicable.
References
Alameer Z, Abd Elaziz M, Ewees AA, Ye H, Jianhua Z (2019) Forecasting copper prices using hybrid adaptive neuro-fuzzy inference system and genetic algorithms. Nat Resour Res 28:1385–1401
Astudillo G, Carrasco R, Fernández-Campusano C, Chacón M (2020) Copper price prediction using support vector regression technique. Appl Sci 10:6648. https://doi.org/10.3390/app10196648
Cai X, Zhang N, Venayagamoorthy GK, Wunsch DC II (2007) Time series prediction with recurrent neural networks trained by a hybrid PSO–EA algorithm. Neurocomputing 70:2342–2353
Catalao JPS, Pousinho HMI, Mendes VMF (2011) Hybrid wavelet-PSO-ANFIS approach for short-term electricity prices forecasting. IEEE Trans Power Syst 26(1):137–144
Dehghani H, Bogdanovic D (2018) Copper price estimation using bat algorithm. Resour Pol 55:55–61. https://doi.org/10.1016/j.resourpol.2017.10.015
Duman S, Yorukeren N, Altas IH (2015) A novel modified hybrid PSOGSA based on fuzzy logic for non-convex economic dispatch problem with valve-point effect. Int J Electr Power Energy Syst 64:121–135
Figuerola-Ferretti I, Gonzalo J (2010) Modelling and measuring price discovery in commodity markets. J Econometrics 158:95–107
Garcia D, Kristjanpoller W (2018) An adaptive forecasting approach for copper price volatility through hybrid and non-hybrid models. Appl Soft Comput 74:466–478
Gilles J (2013) Empirical wavelet transform. IEEE Trans Signal Process 61(16):3999–4010
Gundu V, Simon SP (2021) PSO–LSTM for short term forecast of heterogeneous time series electricity price signals. J Amb Intel Hum Comp 12(2):2375–2385
Hajizadeh E, Mahootchi M, Esfahanipour A, Kh MM (2019) A new NN-PSO hybrid model for forecasting Euro/Dollar exchange rate volatility. Neural Comput Appl 31(7):2063–2071
Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780
Hu Y, Ni J, Wen L (2020) A hybrid deep learning approach by integrating LSTM-ANN networks with GARCH model for copper price volatility prediction. Physica a: Stat Mechanics Appl 557:124907
Huang M-L, Chou Y-C (2019) Combining a gravitational search algorithm, particle swarm optimization, and fuzzy rules to improve the classification performance of a feed-forward neural network. Comput Meth Prog Bio 180:105016
Kennedy J, Eberhart R (1995) Particle swarm optimization. Proc Int Conf Neural Netw (ICNN). pp 1942–1948
Kristjanpoller W, Minutolo MC (2015) Gold price volatility: A forecasting approach using the Artificial Neural Network–GARCH model. Exp Syst Appl 42(20):7245–7251
Lasheras FS, de Cos Juez FJ, Sánchez AS, Krzemień A, Fernández PR (2015) Forecasting the COMEX copper spot price by means of neural networks and ARIMA models. Resour Policy 45:37–43
Li T, Hu Z, Jia Y, Wu J, Zhou Y (2018) Forecasting Crude Oil Prices Using Ensemble Empirical Mode Decomposition and Sparse Bayesian Learning. Energies 11:1882. https://doi.org/10.3390/en11071882
Liu H, Mi X, Li Y (2018) Wind speed forecasting method based on deep learning strategy using empirical wavelet transform, long-short term memory neural network and Elman neural network. Energy Convers Manage 156:498–514
Liu H, Wu H, Lv X, Ren Z, Liu M, Li Y, Shi H (2019) An intelligent hybrid model for air pollutant concentrations forecasting: Case of Beijing in China. Sustain Cities Soc 47:101471. https://doi.org/10.1016/j.scs.2019.101471
Lv L, Kong W, Qi J, Zhang J (2018) An improved long short-term memory neural network for stock forecast. MATEC Web of Conferences 232:01024. https://doi.org/10.1051/matecconf/201823201024
Ma X, Tao Z, Wang Y (2015) Long short-term memory neural network for traffic speed prediction using remote microwave sensor data. Transp Res C 54:187–197
Mahdiani MR, Khamehchi E (2016) A modified neural network model for predicting the crude oil price. Intell Econ 10:71–77
Manickavasagam J, Visalakshmi S, Apergis N (2020) A novel hybrid approach to forecast crude oil futures using intraday data. Technol Forecast Soc Change 158:120126
Mirjalili S, Mohd Hashim SZ, Moradian Sardroudi H (2012) Training feed-forward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Appl Math Comput 218:11125–11137
Mostafa MM, El-Masry AA (2016) Oil price forecasting using gene expression programming and artificial neural networks. Econ Model 54:40–53
Oglend A, Asche F (2016) Cyclical non-stationarity in commodity prices. Empir Econ 51:1465–1479
Peng T, Zhou J, Zhang C, Fu W (2017) Streamflow forecasting using empirical wavelet transform and artificial neural networks. Water 9:406. https://doi.org/10.3390/w9060406
Qiu J, Wang B, Zhou C (2020) Forecasting stock prices with long-short term memory neural network based on attention mechanism. PLoS ONE 15(1):e0227222. https://doi.org/10.1371/journal.pone.0227222
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inform Sciences 179:2232–2248
Rubaszek M, Karolak Z, Kwas M (2020) Mean-reversion, non-linearities and the dynamics of industrial metal prices. A Forecasting Perspective Resour Pol 65:101538
Shabri A, Samsudin R (2014) Daily crude oil price forecasting using hybridizing wavelet and artificial neural network model. Math Probl Eng 2014:201402. https://doi.org/10.1155/2014/201402
Shao B, Li M, Zhao Y, Bian G (2019) Nickel price forecast based on the LSTM neural network optimized by the improved PSO algorithm. Math Probl Eng 2019:1934796. https://doi.org/10.1155/2019/1934796
Su M, Zhang Z, Zhu Y, Zha D, Wen W (2019) Data driven natural gas spot price prediction models using machine learning methods. Energies 12:1680. https://doi.org/10.3390/en12091680
Wang L, Zhang Z (2020) Research on shanghai copper futures price forecast based on X12-ARIMA-GARCH family models. In Proceedings of the 2020 International Conference on Computer Information and Big Data Applications (CIBDA), Guiyang. Guiyang, China, pp 304–308
Watkins C, McAleer M (2002) Cointegration analysis of metals futures. Math Comput Simulat 59:207–221
Wu Q, Lin H (2019) Daily urban air quality index forecasting based on variational mode decomposition, sample entropy and LSTM neural network. Sustain Cities Soc 50:101657
Yazdani-Chamzini A, Yakhchali SH, Volungevičienė D, Zavadskas EK (2012) Forecasting gold price changes by using adaptive network fuzzy inference system. J Bus Econ Manag 13(5):994–1010. https://doi.org/10.3846/16111699.2012.683808
Yu P, Yan X (2020) Stock price prediction based on deep neural networks. Neural Comput Appl 32(6):1609–1628. https://doi.org/10.1007/s00521-019-04212-x
Yuan X, Chen C, Jiang M, Yuan Y (2019) Prediction interval of wind power using parameter optimized Beta distribution based LSTM model. Appl Soft Comput 82:105550
Zhang J, Zhang Y, Zhang L (2015) A novel hybrid method for crude oil price forecasting. Energy Econ 49:649–659. https://doi.org/10.1016/j.eneco.2015.02.018
Acknowledgements
The authors would like to thank Dr. Tu-Son Kim, Faculty of Finance, Kim Il Sung University, the DPR Korea, for the invaluable contribution and stimulating discussions.
Funding
No funding was received for conducting this study.
Author information
Authors and Affiliations
Contributions
Conceptualization, Y.-H. Kim, S.-J. Ham and C.-S. Ri; methodology, Y.-H. Kim, W.-H. Kim and W.-S. Ri; software, Y.-H. Kim and W.-S. Ri; formal analysis, S.-J. Ham and C.-S. Ri; writing–original draft preparation, Y.-H. Kim, S.-J. Ham and C.-S. Ri; writing–review and editing, Y.-H. Kim, S.-J. Ham, C.-S. Ri and W.-H. Kim. All authors have read and approved the final version of the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest.
Additional information
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Kim, YH., Ham, SJ., Ri, CS. et al. Application of empirical wavelet transform, particle swarm optimization, gravitational search algorithm and long short-term memory neural network to copper price forecasting. Port Econ J (2024). https://doi.org/10.1007/s10258-024-00252-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10258-024-00252-x
Keywords
- Copper price forecasting
- Long-short term memory neural network
- Particle swarm optimization
- Gravitational search algorithm
- Empirical wavelet transform