Research on Multicollinearity in the Grey GM(1,N) Model

For the grey GM(1,N) models, due to accumulation and other reasons, multicollinearity can arise between variables, which can cause instability in the model and result in erroneous predictions. Studying this ill-posed problem has important practical significance for improving the prediction accuracy of the GM(1,N) model. Firstly, to diagnose the multicollinearity in the GM(1,N) model, this paper uses the grey relational degree to measure the linear correlation between multiple variables for the GM(1,N) model's less informative characteristics. In addition, the eigenvalue method is used to measure the degree of multicollinearity. Then, in order to address the problem of multicollinearity in the GM(1,N) model, the principal component-ridge regression method (PCRE) is introduced into the GM(1,N) model. The admissibility and superiority of the PCRE method are studied under the balance loss function. Finally, an empirical analysis verified the superiority of the PCRE method in addressing the multicollinearity of the GM(1,N) model.