The kernel-based nonlinear multivariate grey model

The grey models have appealed considerable interest of research due to their effectiveness for time series forecasting with small samples. But most of the existing grey models are essentially linear models, which limits the applicability of the grey models. In this paper, we introduce a novel nonlinear multivariate grey model which is based on the kernel method, and named as the kernel-based GM(1, n), abbreviated as the KGM(1, n). The KGM(1, n) model contains an unknown function of the input series, which can be estimated using the kernel function, and then the KGM(1, n) model is available to describe the nonlinear relationship between the input and output series. The case studies of predicting the oilfield production, the condensate gas well production and coal gas emission are carried out, and the results show that the KGM(1, n) model is much more efficient than the existing linear multivariate grey models and the LSSVM. The nonlinearity of KGM(1, n), the effects of the data structure, the sample size and the prediction term on the KGM(1, n) model have also been discussed combined with the theoretical analysis and the numerical experiments.