Reliable novel hybrid extreme gradient boosting for forecasting copper prices using meta-heuristic algorithms: A thirty-year analysis

Forecasting copper price accurately is essential in various aspects of economics. However, due to the complex and unpredictable fluctuations in copper prices make this task quite challenging. Then, the goal of the current study is to develop a novel hybrid intelligence method, namely SSO-XGB and HHO-XGB models, to accurately forecast copper prices in the future by utilizing extreme gradient boosting (XGB) and three metaheuristic algorithms – sparrow search optimization (SSO) and harris hawk optimization (HHO). To do this, time series datasets of copper prices over a 30-year period (1993–2023) were collected, taking into account influencing factors including aluminum, natural gas, gold, crude oil, silver, iron ore, and nickel prices, as well as exchange rates of the most significant countries. The XGB model's hyperparameters were fine-tuned by the SSO and HHO algorithms to achieve accurate copper price forecasts. In addition, comparative models were developed using the traditional XGB (optimized by grid search) model and gene expression programming (GEP) to obtain convincing experimental results for the proposed SSO-XGB and HHO-XGB models. Among these, the SSO-XGB model demonstrated the highest level of accuracy, achieving an RMSE, AARE, R2, and MAE of 106, 4.59, 0.992, and 58 respectively on the training data. Additionally, the sensitivity analysis (measured through mutual information (MI)) revealed that changes in gold and crude oil prices significantly impacted the copper price. In general, all four intelligence methods evaluated in this study demonstrated an acceptable level of performance for predicting copper prices.