A novel kernel regularized nonhomogeneous grey model and its applications

The nonhomogeneous grey model (NGM) is a novel tool for time series forecasting, which has attracted considerable interest of research. However, the existing nonhomogeneous grey models may be inefficient to predict the complex nonlinear time series sometimes due to the linearity of the differential or difference equations based on which these models are developed. In order to enhance the accuracy and applicability of the NGM model, the kernel method in the statistical learning theory has been utilized to build a novel kernel regularized nonhomogeneous grey model, which is abbreviated as the KRNGM model. The KRNGM model is represented by a differential equation which contains a nonlinear function of t. By constructing the regularized problem and using the kernel function which satisfies the Mercer's condition, the parameters estimation of KRNGM model only involves in solving a set of linear equations, and the nonlinear function in the KRNGM model can be expressed as a linear combination of the Lagrangian multipliers and the selected kernel function, and then the KRNGM model can be solved numerically. Two case studies of petroleum production forecasting are carried to illustrate the effectiveness of the KRNGM model, comparing to the existing nonhomogeneous models. The results show that the KRNGM model outperforms the existing NGM, ONGM, NDGM model significantly.