Forecasting the multifactorial interval grey number sequences using grey relational model and GM (1, N) model based on effective information transformation

Abstract

In the context of data eruption, the data often show a short-term pattern and change rapidly which makes it difficult to use a single real value to express. For this kind of small-sample and interval data, how to analyze and predict multi-factor sequences efficiently becomes a problem. By this means, grey system theory (GST) is developed in which the interval grey numbers, as a typical object of GST, characterize the range of data and the grey relational and prediction models analyze the relations of multiple grey numbers and forecast the future. However, traditional grey relative relational model has some limitations: the results obtained always show low resolution, and there are no extractions for the interval feature information from the interval grey number sequence. In this paper, the grey relational analysis model (GRA) based on effective information transformation of interval grey numbers is established, which contains comprehensive information of area differences and slope variances and optimizes the resolution of traditional grey degree. Then, according to the relational results, the multivariable GM model (GM (1, N)) is proposed to forecast the interval grey number sequence. To verify the effectiveness of this novel model, it is established to analyze the relationship between the degree of traffic congestion and its relevant factors in the Yangtze River Delta of China and predict the development of urban traffic congestion degrees in this area over the next 5 years. In addition, some traditional statistical methods (principal component analysis, multiple linear regression models and curve regression models) are established for comparisons. The results show high performances of the novel GRA model and GM (1, N) model, which means the models proposed in this paper are suitable for interval grey numbers from regional data. The strengths which recommend the use of this novel method lie in its high recognition mechanism and multi-angle information transformation for interval grey numbers as well as its characteristic of timeliness in information processing.