Improvement To GM(1, 1) Model And Research On Grey Statistical Models

In modern society's economic activity, scientific research activity as well as in people's daily life, Uncertain information exits everywhere obviously. Grey system theory is a new method, which has been used to research uncertain problem lack of data and information. Through researching information which we gave known, we can get what we need. Grey System Theory can be used to study uncertain or a few swatch or deficient informstion system, some of its information is known and some is unknown. Grey System Theory has been used widely. This paper deeply studies Grey System Theory, and puts forward some new solutions to GM(1,1) model and new forecasting model. The paper is divided into six chapters as follow:Chapter one, Introduction. We discusses the goal and meaning of the research. In this part, we also introduce several uncertain methods.We discusses Grey System Theory and the domestic and foreign research on this theory in detail .We give the main content, technological route and methods.Chapter two, Grey System Theory's Basic Concepts. This part gives Grey System Theory's basic concepts: Sequence operator, Sequence smooth condition, Grey exponent law and so on. This is the foundation of grey modeling.Chapter three, Grey forecast model GM (1,1) and method system. This part introduces GM(1,1) modeling mechanism and types of GM(1,1) model which includes Residual error GM(1,1) model ,Partial-data GM(1,1) model and Metabolic GM(1,1) model. It also gives the application situation about all kinds of grey models, the general forecast process with GM(1,1) model.Chapter four, improvement to GM(1,1) model and Grey Exponential Smoothing Model. First this chapter describes the necessity of model improvement, proposes improvement to Gm(1,1) model: Integrated the improvement background value and the starting value method. Second Considering traditional GM (1,1) model entrusts with the primitive sequence same power value, but the index smoothly through smoothly entrusts with the primitive sequence to the primarydata to be different the weight, proposed the pessimistic index smooth model. And the union example had proven this article proposed model feasibility.Chapter five, Grey statistical model research. The statistical analysis is one of the most widespread used methods. The system is composed by the multi- essential factors, we can not obtain the very good result sometimes by solely studing the system main characteristic, but GM (1,1) model mainly is considered the system main characteristic.This work establishes GM(1,1) model to the system major factor by integrating two merits, then carries on the regression analysis to the gray simulation value, and the model which established with other researchers has conducted the contrast research. In the example analysis we model the Jilin Province agricultural economy total output value; We have the more system's indexs, we can know the system the better. But we have to do more things to get the more indexs. Sometimese obtaining all indexs to be difficult, analyzing the data also to have the difficulty.This paper uses the principal components analytic method to reduce the system dimension, first carries on accumulation operator processing to the primary data, then takes the processing data as the principal components analysis the primary data, finally carries on the regression analysis to the principal components accumulation value and the dependent variable accumulation value, established the grey principal components model. The example proves the method validity.Chapter six, Conclusions and expectations of the paper. Mainly introduced the present paper innovation , along with system research thorough, forecasts to the grey system theory further studies.