Discrete-Time Grey Endogenous Models

Summarizing the continuous-time grey endogenous model outlined in Chapter 3 , we can briefly describe the modeling process as follows: discrete (point observation) \(\rightarrow \) continuous (time-responsive) \(\rightarrow \) discrete (point prediction). The inevitable transition between continuous and discrete introduces errors. Deriving a direct modeling approach without the need for “continuous (time-responsive)” discretization holds the promise of enhancing model accuracy (Wang et al. 2020). Viewing from the perspective of “discrete (point observation) \(\rightarrow \) discrete (point prediction)” (Xie and Liu 2005), researchers have started from the continuous-time grey GM(1,1) model and derived the discrete-time grey DGM(1,1) model, establishing a modeling paradigm for discrete-time grey systems. Subsequently, some scholars have proposed discrete-time grey endogenous forecasting model models suitable for different time series characteristics, yielding a series of outstanding theoretical and applied achievements.