Data-based structure selection for unified discrete grey prediction model

Grey models have been reported to be promising for time series prediction with small samples, but the diversity kinds of model structures and modelling assumptions restrains their further applications and developments. In this paper, a novel grey prediction model, named discrete grey polynomial model, is proposed to unify a family of univariate discrete grey models. The proposed model has the capacity to represent most popular homogeneous and non-homogeneous discrete grey models and furthermore, it can induce some other novel models, thereby highlighting the relationship between the models and their structures and assumptions. Based on the proposed model, a data-based algorithm is put forward to select the model structure adaptively. It reduces the requirement for modeler's knowledge from an expert system perspective. Two numerical experiments with large-scale simulations are conducted and the results show its effectiveness. In the end, two real case tests show that the proposed model benefits from its adaptive structure and produces reliable multi-step ahead predictions. (C) 2019 Elsevier Ltd. All rights reserved.