Structural extension and parameter optimization of multivariable grey prediction model with real-number order and its application

Purpose To address the modeling challenge posed by complex systems that exhibit linearity, nonlinearity, local oscillations and long-term trends. Design/methodology/approach The Euler polynomial, linear correction term and grey action quantity term are simultaneously introduced to extend the structure of the traditional multivariable grey prediction model. A variable-structure adaptive multivariable grey prediction model is then constructed. Furthermore, the model’s performance is enhanced through the differential design and optimization of the accumulation orders for the dependent and independent variables, as well as the background value coefficients. Findings The proposed model is applied to simulate and predict the quarterly total electricity consumption in Guangzhou. The results show that the new model significantly outperforms several existing grey prediction models in terms of both accuracy and stability. Originality/value This study contributes to the further development and enrichment of multivariable grey prediction methodology, providing a novel approach for modeling complex systems characterized by local oscillations and long-term trends.