Research on the novel recursive discrete multivariate grey prediction model and its applications

• We propose a novel multivariate grey prediction model RDGM(1, n).
• The RDGM(1, n) is approximately identical to GMC(1, n) only when |b1| is small.
• The GMC(1, n) would be inaccurate when |b1| is not small.
• The accuracy of RDGM(1, n) is not limited to the values of its parameters.
• RDGM(1, n) outperforms GMC(1, n) in the numerical examples.

The grey system is an efficient tool to deal with uncertain problems. The prediction models of grey system are quite popular and have been utilised in a wide variety of fields. The GMC(1, n) model is a novel multivariate grey prediction model with correct solution, which has attracted considerable interest, but the accuracy of GMC(1, n) still needs to be improved. In this paper, a novel multivariate grey prediction model called the recursive discrete multivariate grey prediction model is proposed based on the whiten equation of GMC(1, n) model and recursive method , which is abbreviated as RDGM(1, n). The relationship and difference between the RDGM(1, n) and GMC(1, n) are discussed with mathematical analysis, and the reason why the GMC(1, n) is not accurate in some applications is also revealed. Three numerical examples are carried out to assess the effectiveness of the RDGM(1, n) in comparison with the conventional GMC(1, n) with two forms of discrete solutions. It is shown in the numerical results that the RDGM(1, n) outperforms the existing GMC(1, n) in most cases.