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Based on the reason that the growth of discrete grey model is constant, the paper structured quadratic time-varying parameters discrete grey model (referred to as QDGM(1,1)) by introducing quadratic time-varying terms. And then the paper researched properties of the new model, and reached the conclusion that QDGM(1,1) possessed white exponential law coincidence, linear law coincidence, quadratic law coincidence and consistency of stretching transformation. What's more, the paper applied optimization method to optimizing the iterative starting value of the new model, and introduced the steps of using QDGM(1,1) to predict. Finally, the new model was compared with another three discrete grey models through an instance. It was proved that the new model greatly improves the simulation and prediction precision. [ABSTRACT FROM AUTHOR]

In order to further complement the system of grey power models, this paper analyzes the transformation relationships between the classic GM(1,1) model and GM(1,1) power model, and deduces five derived models including GM(1,1,x(2)) power model, GM(1,1,x(1)) power model, GM(1,1,6) power model, GM(1,1,exp) power model and GM(1,1,C) power model based on the defined and whitened GM(1,1) power models. A group of grey power models including classic GM(1,1) power model and the derived five models is built finally. The results show that time response functions of GM(1,1) model and GM(1,1) power model are essentially the same. Different derived models have different structures, contents and solutions, reflecting the principal of non-unique solution in grey system theory. In practical applications, the most appropriate whitened solution can be identified from group of default solutions under the corresponding objectives. [ABSTRACT FROM AUTHOR]