Application of empirical wavelet transform, particle swarm optimization, gravitational search algorithm and long short-term memory neural network to copper price forecasting

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 $$p$$ 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.