Unified novel multivariate discrete grey model with cumulative time effect

Grey system models have been widely used in various areas and disciplines, and the incorporation of time effects into grey system models is confirmed to be an effective method in handling series with nonlinear characteristics. The task of model identification is becoming more difficult with the emergence of various models with time effects. To this end, a unified novel multivariate discrete grey model with cumulative time effect, namely CTDGM(1,N), is proposed by integrating mainstream time effects and conventional multivariate discrete grey model. Ideally, most existing grey model involving time effects can be derived from the novel model by taking different parameters. Specifically, the cumulative time effect is introduced to identify the nonlinear characteristics in time series. Furthermore, affine properties and uniformity analysis are conducted to assist in understanding the modelling mechanism. The numerical results show the novel model outperforms other benchmarks and could be considered a promising approach for forecasting renewable power generation in China.