Grey prediction models have been widely used in various fields of society due to their high prediction accuracy; accordingly, there exists a vast majority of grey models for equidistant sequences; however, limited research is focusing on nonequidistant sequence. The development of nonequidistant grey prediction models is very slow due to their complex modeling mechanism. In order to further expand the grey system theory, a new nonequidistant grey prediction model is established in this paper. To further improve the prediction accuracy of (...) the NEGM model, the background values of the improved nonequidistant grey model are optimized based on Simpson formula, which is abbreviated as INEGM. Meanwhile, to verify the validity of the proposed model, this model is applied in two real-world cases in comparison with three other benchmark models, and the modeling results are evaluated through several commonly used indicators. The results of two cases show that the INEGM model has the best prediction performance among these competitive models. (shrink)

The grey system model with time power, which is often called the GM, appeals considerable interest of research due to its effectiveness in time series forecasting. Aimed to improve further the GM model, this paper introduces a new whitening equation with variable coefficient into the original whitening equation which extends applicable scope; as a result, an improved grey model with time power, namely, OGM, is proposed. Firstly, the time response function of the novel model and the restored values of original (...) series are deduced through grey modelling techniques. Secondly, the variable coefficient in the whitening equation and the time power are determined by particle swarm optimization algorithm. Two empirical examples are then used to verify the validity of the novel model. Finally, the novel model is applied to predict the oil consumption of China from 2004 to 2018. Results show the novel model outperforms other commonly-used competitive models, which can well serve a benchmark model for scholars and decision-makers. (shrink)