A Novel Grey Prediction Model: A Hybrid Approach Based on Extension of the Fractional Order Discrete Grey Power Model with the Polynomial-Driven and PSO-GWO Algorithm

Background: This study addresses the challenge of predicting data sequences characterized by a mix of partial linearity and partial nonlinearity. Traditional forecasting models often struggle to accurately capture the complex patterns of change within the data. Methods: To this end, this study introduces a novel polynomial-driven discrete grey power model (PFDPGM(1,1)) that includes time perturbation parameters, enabling a flexible representation of complex variation patterns in the data. The model aims to determine the accumulation order, nonlinear power exponent, time perturbation parameter, and polynomial degree to minimize the fitting error under various criteria. The estimation of unknown parameters is carried out by leveraging a hybrid optimization algorithm, which integrates Particle Swarm Optimization (PSO) and the Grey Wolf Optimization (GWO) algorithm. Results: To validate the effectiveness of the proposed model, the annual total renewable energy consumption in the BRICS countries is used as a case study. The results demonstrate that the newly constructed polynomial-driven discrete grey power model can adaptively fit and accurately predict data series with diverse trend change characteristics. Conclusions: This study has achieved a significant breakthrough by successfully developing a new forecasting model. This model is capable of handling data sequences with mixed trends effectively. As a result, it provides a new tool for predicting complex data change patterns.