Improvement Of GM(1,1) And Its Application

Through development ofmore than 30 years, the grey system theory has been accepted and recognized as the academic circles at home and abroad, has had a profound impact on the development of systems science. It has the advantages in many aspects, such as the small required sample size, simple operation, high prediction accuracy of short term and so on. It has been widely used in many fields of industry, agriculture, transportation and aerospace, many practicaliy difficult problems can be solved, showing the extremely broad prospect of application. However, as a new and unique theoretical system, it needs to be further improved. Through further improvement and optimization of the grey prediction model to improve the prediction accuracy and expand its scope of application, so that it can further play the excellent characteristics and application potential. This has far-reaching significance. This paper improves, based on analysis of these factors thatinfluence the precision of GM(1, l), in the original data sequence processing, Selection of the background value, the initial value, residual sequence treatment of the GM(1, l), The main contents are as follows:1. For the equal interval GM(1, l), in this paper, the three main factors:the smoothness, the class ratio deviation, the concave convex property of the data sequence are taken into account, discussing their advantages and disadvantages of the power, exponential, logarithmic function andtheir compound function in improving the prediction accuracy of model. Do some innovation in the following aspects(1) Maximum points of concave subsequenceis introduced to the study of the concave convex property of data sequence, expand the scope of the concave convex property application of data sequence for the equal interval GM(1, 1), so it has better maneuverability.(2) Several factors, associated with the model accuracy, are considered comprehensively, the smoothness, the class ratio deviation, the concave convex property of data sequence overcome the instability of the solution brought by the most studies only considering a few factors, improve the stability of the model. The processing steps and application examples are given. The forecast results of the improved model show the method proposed in this paper has good effectin improving the prediction accuracy of the model.2. For the non equal interval GM(1,1), the model was modified by three aspects: the background value, the initial value and the residual. The main innovation is(1) for the non equal interval GM(1,1), gives modified form of initial value:, the coefficient to be determined. difference polynomial is introduced to the construction of the background value.(2) The data sequence mapping methodis given from the data sequence it was positive or negative not determined to a non negative increasing data sequence, to avoid low forecasting precision limitation of the volatility series. Then put forward a method of comprehensive improvement to non equal interval GM(1,1) and use the method to example modeling, the prediction results show the effectiveness of the improved method proposed in this paper.