Forecasting China's shipping indices based on modal decomposition and optimized deep learning integrated model.

This study proposes an innovative hybrid forecasting model, VMD-CPSO-BiLSTM, which significantly enhances the prediction accuracy of shipping indices in China's maritime sector. The model employs a sophisticated three-phase methodology: (1) decomposition through Variational Mode Decomposition (VMD) to extract multiple intrinsic mode functions (IMFs) from the original time series, effectively capturing its nonlinear and complex patterns; (2) optimization using a Chaotic Particle Swarm Optimization (CPSO) algorithm to fine-tune the Bi-directional Long Short-Term Memory (BiLSTM) network parameters, thereby improving both predictive accuracy and model stability; and (3) integration of predictions from both high-frequency and low-frequency components to generate comprehensive final forecasts. Through extensive empirical validation using key Chinese shipping indices, our proposed model demonstrates superior performance compared to conventional single deep learning models and other hybrid approaches. The results indicate that VMD-CPSO-BiLSTM effectively addresses critical challenges in time series forecasting, including nonlinearity, non-stationarity, and multi-scale characteristics. The developed model offers substantial practical value as a reliable forecasting tool for shipping market trends, providing industry stakeholders with enhanced decision-making support for strategic planning and operational management. Its robust performance and methodological innovation contribute significantly to the field of maritime economics and financial time series analysis.