Research On Construction, Expansion And Application Of The Generalized Gm(1,1) Forecast Model

The grey system theory which is characteristic as one new theory has the huge function and the profound influence to the scientific progress and has been recognized in the domestic and foreign academic circle. Especially, the gray prediction theory has been applied in many scientific fields including the agriculture, the industry, the energy, the economy, the society and so on in the short more than 20years, by which a lot of actual problems in the production, the life and the scientific research massive were successfully solved.At present, the application and research of the grey prediction model and the GM(1,1) forecast model was very already common in domestic and foreign.Some scholars researched the GM(1,1) forecast model from the theoretical view and a lot of new method and theory were obtained, specially in the transformation between the primitive equation and the differential equation or difference equation. The GM(1,1) difference model was proposed by one scholar and obtained academic circle's consistent approval and highly praises, which can solve the flaw in the old GM(1,1) forecast model in the index series agonic fitting. But, two different GM(1,1) models that the difference model and the differential model would also caused some problems in the actual utilization of these models. Just for it, the generalized GM(1,1) forecast model was proposed in this paper by deeply researching the foundation in the difference model and the differential model. And some natures of this new model were researched in detail such as the generality nature, the optimization nature, the unbiased nature to fit the pure indexes and so on. The generality and the optimization of the generalized GM(1,1) forecast model were fully reflected by comparing the different natures in these models. The second, three common expansion method in the grey forecast model were unified with the generalized GM(1,1) forecast mode, namely the residual revises, the metabolism method as well as the cushion operator data processing method, and the corresponding generalized GM(1,1) unified model were proposed. Finally, a similar example was utilized to reflect the results by using different models including the differential GM(1,1) forecast model, the difference GM(1,1) forecast model as well as the generalized GM(1,1) forecast model in the fifth chapter of this paper. Of course, the conclusion of academic was provided by the example computation which is the generalized GM(1,1) forecast model is the best model between three GM(1,1) models. The residual generalized GM(1,1) model revision method which was used in the he residual revision model could effective enhancement the precision in fitting and forecasting in the same example, and simultaneously the revision method limitation also was confirmed. The theory value and the practical significance of the generalized GM(1,1) forecast model and the expansion method were fully proven by the example application. Then, there are enough reasons to believe that this new model and the expansion method would produce certain function to the gray forecast model theory and its further consummation.