Application of a Stacking Model with Multiple Base Learners Optimized by an Slime Mold Algorithm for Container Freight Index Prediction

Abstract

Accurate prediction of container freight rate indices is crucial for the sustainable development of the shipping industry. However, existing forecasting models often suffer from limitations such as insufficient prediction accuracy and poor model interpretability. To address these issues, this paper proposes a hybrid forecasting model based on the Stacking framework. First, Lasso regression, combined with the partial autocorrelation function (PACF), is employed to identify the key influencing factors and historical freight rate indices, thereby constructing a prediction indicator system. Next, within the Stacking framework, appropriate base learners and a meta-learner are selected, and the slime mold optimization algorithm (SMA) is applied for automated parameter tuning of individual models. Furthermore, regularization techniques, cross-validation, and early stopping mechanisms are introduced to effectively prevent model overfitting. To validate the model’s effectiveness, experiments are conducted using three data sets: the China Containerized Freight Index (CCFI), the Shanghai Containerized Freight Index (SCFI), and the Ningbo Containerized Freight Index (NCFI). The SHAP method is used to explain the prediction results and to conduct an in-depth analysis of the key factors influencing the Container Freight Rate Index. The experimental results demonstrate that the proposed hybrid model improves prediction accuracy by 16.43% compared with single forecasting models. This model exhibits significant advantages in handling complex market environments, and it enhances both robustness and interpretability, offering a new tool for practical applications.