The grey multivariate forecasting model based on seasonal fluctuation series and its application

Purpose To address forecasting challenges of seasonal and nonlinear time series data, this study proposes a seasonal multivariate discrete grey power model with power exponents, trigonometric functions and time power terms to improve prediction accuracy. Design/methodology/approach Firstly, the SDPGM(1,N) model is built with trigonometric functions and time power terms. Next, particle swarm optimization is utilized to calculate the nonlinear parameters, enhancing the model’s forecasting accuracy. Finally, the model is applied to the quarterly solar energy generation forecast in China and compared with other commonly used models. Findings Results show SDPGM(1,N) outperforms three other grey models as well as statistical and machine learning models. This highlights its ability to fit and predict complex seasonal data, proving its practical utility. Practical implications Accurate forecasting of China’s quarterly solar power generation is imperative for informing strategic adjustments in energy policy and for guiding the industry planning within the solar power sector. Originality/value Using trigonometric functions and time power terms is a good way to handle seasonal and nonlinear data. It has been used to forecast China’s quarterly solar power generation. This method uses the periodic nature of trigonometric functions to capture seasonality and the flexibility of time power terms to model nonlinear trends, improving prediction accuracy in the solar power sector.