Purpose This paper aims to propose an improved seasonal fractional order discrete grey multivariate model to more accurately predict data series with seasonal and periodic characteristics. Design/methodology/approach A seasonal differentiated fractional order grey multivariate model considering interaction effect is constructed by introducing interactive and seasonal driving terms, as well as differentiated accumulative orders. The new model considers the interaction effect between the transverse and longitudinal evolution. Moreover, differentiated accumulation orders are set for heterogeneous variables. To further enhance the model, an average weakening buffer operator is further introduced. Secondly, the optimal algorithm is screened through the Monte Carlo method. The robustness and noise sensitivity are analyzed through comparative analysis and statistical tests. Finally, the new model is applied to the quarterly sales of new energy vehicles in China. Findings Validation results demonstrate significant advantages of the novel model for seasonal and cyclical data, exhibiting minimal error, highest stability, and lowest noise sensitivity. In addition, the results of predicting the future quarterly sales of new energy vehicles demonstrate a year-by-year increase in sales and a gradual decrease in periodic volatility. Originality/value The new model integrates interaction, seasonality, and differentiated accumulation orders, demonstrating strong fitting and forecasting capabilities for seasonal and periodic data. Additionally, it can be effectively used to forecast new energy vehicle quarterly sales in China, aiming to provide more precise data support for automakers to optimize production capacity allocation and enhance supply chain collaboration.
Li et al. (2025) studied this question.