Spatio-temporal grey Bernoulli model for green development of marine economy forecasting

The sustainable development of the marine economy is inseparable from green development. However, the spatial correlations and dynamic evolution of green development present significant forecasting challenges. To address this, this paper first constructs an evaluation index system for the green development of marine economy based on the Driver-Pressure-State-Impact-Response ( DPSIR ) framework. Furthermore, the grey Bernoulli model is improved in both spatial and temporal dimensions for forecasting purposes. Interaction terms between spatial distance matrices and variables are introduced to capture spatial correlations, while a time-varying component is incorporated to reflect dynamic evolution. These enhancements enable the model to more effectively characterize the spatial, temporal, and nonlinear features of the green development of marine economy. Additionally, the model’s hyperparameters and weighting coefficients are optimized using the whale optimization algorithm. For validation, an empirical study is conducted across China’s 11 coastal provinces and municipalities. Systematic analyses show that the proposed model has high predictive accuracy. Robustness tests and sensitivity analysis further confirm that the model demonstrates excellent stability, reliability, and generalization capability.