Research on a novel kernel based grey prediction model and its applications

Abstract

The discrete grey prediction models have attracted considerable interest of research due to its effectiveness to improve the modelling accuracy of the traditional grey prediction models. The autoregressive GM(1,1) model, abbreviated as ARGM(1,1), is a novel discrete grey model which is easy to use and accurate in prediction of approximate nonhomogeneous exponential time series. However, the ARGM(1,1) is essentially a linear model; thus, its applicability is still limited. In this paper a novel kernel based ARGM(1,1) model is proposed, abbreviated as KARGM(1,1). The KARGM(1,1) has a nonlinear function which can be expressed by a kernel function using the kernel method, and its modelling procedures are presented in details. Two case studies of predicting the monthly gas well production are carried out with the real world production data. The results of KARGM(1,1) model are compared to the existing discrete univariate grey prediction models, including ARGM(1,1), NDGM(1,1,k), DGM(1,1), and NGBMOP, and it is shown that the KARGM(1,1) outperforms the other four models.