Commodity futures basis prediction based on the VMD–DBO–BiGRU model

Considering the nonlinear and nonstationary characteristics of the basis, this paper proposes an ensemble model that integrates Variational Mode Decomposition (VMD), Dung Beetle Optimization (DBO), and Bidirectional Gated Recurrent Units (BiGRUs). To avoid the limitations of a single commodity and to verify the effectiveness of the proposed model, this study selects six futures varieties and analyzes models such as BP (Backpropagation), LSTM (Long Short-Term Memory), DBO–BiGRU, and VMD–BiGRU. The results demonstrate that the VMD–DBO–BiGRU model exhibits superior performance in both one-step and multi-step forecasting. It also confirms the significant effects of VMD and DBO in enhancing the accuracy and stability of predictions. Moreover, models that account for the lag factors of the basis outperform those considering other factors, exhibiting lower errors and higher fit indices.