Grey Compositional Data's Application In A Class Of Economic Structure

This paper researches compositional data's application in a class economical structure of China. Compositional data, which can be used to express industrial structure, households' consumptive structure and so on, is applied in economy more and more broadly. However, compositional data has constant sum and does't obey the normal distribution, which causes great difficulties in its statistical analysis. And the traditional statistical methods are no longer fit for forecasting and analyzing it.Grey System Theory researches the uncertain system of "few sample", "poor information" and "partial information known, partial information unknown" . Through generating and exploring the known information, we could understand the real world, grasp its running behavior and describe the system's evaluative rule exactly by using Grey System Theory. Because Grey System Theory demands less data and can leave out of consideration of data's distribution, and the data samples of the Chinese economical structure are very few, this paper tries to analyze and forecast compositional data by using it.Firstly, based on the symmetrical Logratio transformation and the method of superior analysis in Grey System Theory, this paper builds a model to analyze the magnitude of the relation between two groups of compositional data. Because of the symmetry of the transformation, the transformed variable can reflect the meaning of the original variable better, and this model is easier to be explained. By using this model, this paper analyzes the relation between the Chinese industrial structure and the structure of fiscal expenditure. The validity and rationality of this model are verified by the results. Secondly, based on the symmetrical Logratio transformation similarly, this paper analyses the Chinese urban households' expending structure by using the method of grey principal components analysis, which gets the better result of dimensionality reduced and the reasonable conclusion. Finally, this paper builds a compositional data's forecasting model based on generalized hyperspherical transformation and residual error amendatory GM(1,1) model. And this paper forecasts Chinese industrial structure's developmental trend by using this model. Having been tested, this model has a higher precision.Compared with the actual condition, we conclude that the three models given by this paper can reflect the compositional data's mechanism successfully, and have rational and effective functions of analyzing trend and forecasting.