Discrete grey forecasting model and its optimization.

*(English)*Zbl 1168.62380Summary: Although the grey forecasting model has been successfully adopted in various fields and demonstrated promising results, the literatures show its performance could be further improved. For this purpose, this paper proposes a novel discrete grey forecasting model termed DGM model and a series of optimized models of DGM. This paper modifies the algorithm of \(GM(1, 1)\) model to enhance the tendency catching ability. The relationship between the two models and the forecasting precision of the DGM model based on the pure index sequence is discussed. Further studies on three basic forms and three optimized forms of the DGM model are also discussed. As shown in the results, the proposed model and its optimized models can increase the prediction accuracy. When the system is stable approximately, DGM model and the optimized models can effectively predict the developing system. This work contributes significantly to improve grey forecasting theory and proposes more novel grey forecasting models.

##### MSC:

62M20 | Inference from stochastic processes and prediction |

62M99 | Inference from stochastic processes |

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\textit{N.-M. Xie} and \textit{S.-F. Liu}, Appl. Math. Modelling 33, No. 2, 1173--1186 (2009; Zbl 1168.62380)

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