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The discrete grey modelling technique is a novel methodology of grey predictionmodels, which is effective to improve the effectiveness and applicability of greymodels. In order to build a more general and effective univariate grey predictionmodel, the discrete grey modelling technique is utilised in this paper to builda quadratic polynomial discrete grey model, abbreviated as the QPDGM. Theproperties of the QPDGM model have been discussed, which indicate that thenew model can be regarded as an extension of the conventional discrete greymodel and nonhomogeneous grey model, and it is also coincidence with threeclasses of exponential sequences. The QPDGM model is finally applied to predictthe energy consumption of China, including the electric power, crude oil andnatural gas consumptions. The results have been compared to some commonlyused univariate grey prediction models, which indicates the QPDGM model isgenerally more accurate than other models.

Energy consumption plays a key role in economics development for all countries. Catching the future trend of energy consumption is very important for the governments and energy companies. In this paper, the primary energy consumption of Saudi Arabia, India, Philippines and Vietnam are systematically studied by various forecasting models. Based on the actual data from 2006 to 2016, a novel grey forecasting model termed NDGM_S (1,1,k,c) is proposed where the Simpson numerical integration formula is applied to construct the background value. The time response function and the restored value of the present model are deduced, and then the unbiased property is proved. As shown in the computational results, the NDGM_S (1,1,k,c) model can achieve better prediction accuracy than other forecasting models, and it is quite suitable for predicting sequence with homogeneous/non-homogeneous exponential law.