Understanding cumulative sum operator in grey prediction model with integral matching

Grey prediction models have been widely used in various fields and disciplines. Cumulative sum operator, also called accumulative generation operator, is an essential step in grey modelling, but until now relatively limited attention has been paid to its mechanism of action. In this paper, we introduce the integral matching to explain it. By using the integral transformation, the grey prediction model whose nature is modelling the cumulative sum series with a differential equation proves to be equivalent to that modelling the original series with a reduced differential equation. The cumulative sum operator is the discretization and approximation of the definite integral terms by using the piecewise constant integral and thus can be improved by using the piecewise linear integral. Simulation studies detail the advantages in terms of the stability and robustness to noise. (C) 2019 Elsevier B.V. All rights reserved.