Proposing two novel hybrid intelligence models for forecasting copper price based on extreme learning machine and meta-heuristic algorithms

Abstract

The focus of this study aims at developing two novel hybrid intelligence models for forecasting copper prices in the future with high accuracy based on the extreme learning machine (ELM) and two meta-heuristic algorithms (i.e., particle swarm optimization (PSO) and genetic algorithm (GA)), named as PSO-ELM and GA-ELM models. Accordingly, the time series datasets of the copper price for thirty years were collected based on the influencing parameters, such as crude oil, iron ore, gold, silver, and natural gas prices. Furthermore, the exchange rate of the four largest countries in copper-producing, including Chile (USD/CLP), China (USD/CNY), Peru (USD/PEN), and Australia (USD/AUD), were also considered to evaluate the copper prices. The GA and PSO algorithms then optimized the weights and biases of the ELM model to reduce the error of the ELM model for forecasting copper price. The traditional ELM model (without optimization), and artificial neural networks (ANN) were also developed as the comparative models for resulting in convincing experimental results in the proposed PSO-ELM and GA-ELM models. The results indicated that the proposed hybrid PSO-ELM and GA-ELM models could forecast copper price with higher accuracy and reliability over the traditional ELM and ANN models. Of those, the PSO-ELM yielded the most dominant accuracy with a root-mean-squared error (RMSE) of 304.943, mean absolute error (MAE) of 241.946, mean absolute percentage error (MAPE) of 0.037, and mean absolute scaled error (MASE) of 0.933. The t-test and Wilcoxon test also demonstrated the statistical significance of the proposed models and the best 95% confident interval of the PSO-ELM model with the range of $177.046 to $67.054 with p-value = 2.589e-05. Whereas, the GA-ELM model provided the forecasted copper price higher $137.233 than the actual copper price, and the 95% confidence interval is from $189.672 to $84.793 with p-value = 1.027e-06.