Study On The Characteristics And Optimization Of GM(1, 1) Model

This thesis takes GM (1,1) model as the main, the core of which consists of three parts, namely characteristics of GM (1,1) model, optimization of GM (1,1) model and GM (1,1) Power Model. In each part, relevant models are implemented to further improve the theoretical system of GM and expand the implementation fields of the GM forecast theories and methods. The contents include the following aspects:1.In this paper, some preliminary researches on the morbidity problem of GM has been done. Results from a series of mathematical deduction, with the implementation of eigenvalue estimation theorems from matrix theory, show that the morbidity problem could only exist in GM (1,1) when the first item of original sequence is unequal to zero while other items are equal to zero approximatively. Accordingly, there's no practical meaning to predict by this kind of sequence.2.Analyzing the relations between the stability of GM (1,1) and the development coefficient ? a, taking into account the reality of the nonlinear system, this paper introduces nonlinear item into Unbiased model GM (1,1) and then deduce its logistic expression. Based on the expression, the steady state, periodic state and chaotic characteristics of Unbiased model GM (1,1) are analyzed. Finally, the superiority of Unbiased model GM (1,1) are well explained with chaos theory.3.With the aim of minimizing the errors of simulation value of original data sequence and the sequence, this paper finds the constant number c in the time response sequence of whiterization equation of GM (1,1). Thereby it creates the optimum time response sequence of whiterization equation for GM (1,1) while primary information is well utilized.4. Based on the geometrical sense of the background value of the GM (1,1) model, this paper synthesizes the 1-accumulated sequence with function with non-homogeneous exponential law and introduce a new method for modeling the background value and a more reasonable equation for computing computing the background value . With these new ideas, it successfully enhances the optimized stimulation model and the accuracy of forecast. It's interesting to note that it still maintain a high accuracy when the absolute value of development coefficient is relatively large.5. Based on the analysis of existing problems of the grey Verhulst model and the forms of Whitenization differential equation, this paper uses trapezoid formula to whiten the grey derivative item and educe a new grey Verhulst model, causing a better uniformity of parameters between the difference equation and differential equation in the grey model.6. Based on the basic principle of information overlaping in the grey system, this paper educes the estimate arithmetic of parameterαin GM (1,1) power model. Accordingly how different values of parameterαinfluence the character of model solution is discussed. Simultaneously it supplements the theorem of the solution to whitenization differential equation and presents new methods to optimize the model solution, which further broadens the implementation of the GM (1,1) Power Model.