Abstract: To address the prediction of time series characterized by periodic oscillation, nonlinear trends, and uncertain system behavior, this paper proposes a novel time-varying oscillatory fractional-order TFOGM(1,N, ) power model. Firstly, it adaptively adjusts the accumulation order of independent and dependent variables based on fractional-order calculus. Secondly, trigonometric functions with integer rounding and time power terms are introduced to capture the oscillatory and nonlinear features of the time series, while dummy variables are utilized to quantify policy impacts. Subsequently, by comparing various intelligent algorithms, an optimal algorithm is selected for global hyperparameter optimization. Finally, the model accuracy is validated through a core case study on monthly carbon dioxide emissions in China, supplemented by a case on quarterly solar power generation. Empirical results show the model significantly outperforms comparative models in accuracy, robustness and generalization, with excellent practicality and reliability.

Key words: Grey multivariate prediction, Fractional order accumulation, Virtual variable, Periodic oscillation, Carbon emissions