On unified framework for nonlinear grey system models: An integro-differential equation perspective

Nonlinear grey system models, serving to time series forecasting, are extensively used in diverse areas of science and engineering. However, most research concerns improving classical models developing novel relatively limited attention has been paid the relationship among modelling mechanism. The current paper proposes a unified framework reconstructs model from an integro-differential equation perspective. First, we propose methodological that subsumes various nonlinear as special cases, providing cumulative sum series-orientated paradigm. Then, by introducing integral operator, is reduced equivalent equation; on this basis, structural parameters initial value estimated simultaneously via matching approach. procedure comparison further indicates matching-based provides direct Next, large-scale Monte Carlo simulations conducted compare finite sample performance, results show higher accuracy robustness noise. Applications forecasting municipal sewage discharge water consumption Yangtze River Delta China illustrate effectiveness reconstructed models.