Gray Prediction Model And Its Application

The forecast is to adapt to the socio-economic development and management needs, developed. Prediction as a social practice has been for thousands of years. With the development of human society, the social productive forces has been greatly improved. In particular, the scientific and technological level as the first element of the productivity significantly improve the scientific forecast to gradually replace the forecast of superstition and experience to forecast and develop into a subject. Predictions is the summary of the theoretical generalization of the experience of forecasting activities, it did not last long history. Forecast to truly become a self-contained independent discipline only in recent decades. Traditional forecasting methods is the people engaged in years of research in this area, the prediction methods developed to follow the system in predicting the characteristics and laws, and has played an important role in the major decisions of the national economy..In1982, Prof.J.L.Deng founded the Grey System Theory, Which studies the uncertain system on the "small sample","poor information", i.e."partial information known, partial information unknown" we have. Through creating and excavating the limited information, we could understand the real world, describe its evolvement rule and grasp its running behavior exactly. The Grey System Theory has numerous benefits, such as a little of data, simple principles, convenient operations, having high accuracy in short-term precision, testing and so on. So it has found wide application and made very good progress. But it has limitations as well as another precision. Recent years, many researchers have studied in depth the characteristics of the Grey System Theory for developing its benefits. Considering its better fusional power and penetrability, people try to join the gray model with other models to assay and predict. Combined model can actualize mutual support of relative advantages between different models, avoid the limitations of the single model, amplify the forecast and improve the precision of prediction. Recently, some outcomes are achieved in combined model. But research on combination between grey system and other models is just the beginning, it is necessary to enrich and perfect the theory.Firstly, this paper introduces related theories of Grey System. It mainly includes basic concepts of Grey System, main content, five paces of modeling via, and GM(1,1) which is the most important forecasting model. Secondly, we introduce the central part which is also innovative part. It is devided into two:One part introduces the combined forecast model of gray-linear regressive analysis. Firstly, the independent variables of multiple regressive model are decided by gray correlation analysis. the multiple regressive model is got about data. Considering the multi-collinearlity which is found in designed matrix of regressive model is the innovation. Multi-collinearlity is a common situation in multiple linear regressive. When designed matrix is multi-collinearlity, parameter which is estimated by LS will be unsteady. So the paper incorporates Ridge estimate into combined model to solve multi-collinearlity. Finally, the combined method is applied to forecast the population of old age in Hubei. The accuracy of the model is very good. The combined method is effective.The second part describes the gray combination forecasting model. First dimensional gray fill vacancies in the gray model in the model and the improved long-term forecast model data. Then, according to the model prediction error, using different weights prediction method to determine a combination of weight coefficient of each model. Finally, according to the weighting coefficient to calculate the predictive value of the combined model. This combination model of innovation has the following two points:(1) the gray on gray fill vacancies in the gray model in the model and improved model combination, not only to overcome the shortcomings of accuracy is not high long-term forecasts of the GM (1,1) also combined model can be applied to smooth data sequences to expand the scope of its application.(2)combinations of weight coefficients of the model determines the combined form of the combination model, but also a greater influence to the prediction accuracy of this article with a different weight prediction method to calculate the weight coefficient. Finally, the combined model for the forecast of the number of elderly population in Hubei Province, the results show that the combination of precision of the model prediction accuracy than any single model.