Model GM(1,1,β) and its applicable region

Abstract

Purpose – The paper aims to analyze some properties of GM(1,1,β) model based on the principle that the grey GM(1,1) model parameters are grey and adjustable. Design/methodology/approach – At first, according to the principle that grey GM(1,1) model parameters are grey and adjustable, and the GM(1,1,β) model with parameter packet is put forward. Second, some properties of the GM(1,1,β) model are discussed, and the applicable region of the GM(1,1,β) model is given based on the grey differential equation of the GM(1,1,β) model. At last, the background value coefficient's calculation formula and optimization algorithm of the GM(1,1,β) model are also given. A numeric example is also computed in the last part of the paper. Findings – The result of the study shows that the application scope of the GM(1,1,β) model is (−8,+8). Practical implications – The GM(1,1,β) model provides the theoretical basis for the GM(1,1) model's optimization and can hence forecast its precision. Originality/value – The paper succeeds in realizing the GM(1,1) model's application scope (−2,+2) is broadened to (−8,+8).