Data-based structure selection for unified discrete grey prediction model

Abstract 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.

[1]  Nezih Altay,et al.  OR/MS research in disaster operations management , 2006, Eur. J. Oper. Res..

[2]  Xinping Xiao,et al.  Error and its upper bound estimation between the solutions of GM(1, 1) grey forecasting models , 2014, Appl. Math. Comput..

[3]  Sifeng Liu,et al.  Multi-variable weakening buffer operator and its application , 2016, Inf. Sci..

[4]  Chunyu Yang,et al.  A novel structure-adaptive intelligent grey forecasting model with full-order time power terms and its application , 2018, Comput. Ind. Eng..

[5]  Sophie Ahrens,et al.  Recommender Systems , 2012 .

[6]  Chaoqing Yuan,et al.  On novel grey forecasting model based on non-homogeneous index sequence , 2013 .

[7]  Lifeng Wu,et al.  The effect of sample size on the grey system model , 2013 .

[8]  Sifeng Liu,et al.  Discrete grey forecasting model and its optimization , 2009 .

[9]  Naiming Xie,et al.  Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model , 2015 .

[10]  Sifeng Liu,et al.  Grey system model with the fractional order accumulation , 2013, Commun. Nonlinear Sci. Numer. Simul..

[11]  Qin Liu,et al.  Optimization approach of background value and initial item for improving prediction precision of GM(1,1) model , 2014 .

[12]  Huan Guo,et al.  The modeling mechanism, extension and optimization of grey GM (1, 1) model , 2014 .

[13]  Czesław Cempel,et al.  Using a set of GM(1,1) models to predict values of diagnostic symptoms , 2015 .

[14]  Wei Meng,et al.  A self-adaptive intelligence grey predictive model with alterable structure and its application , 2016, Eng. Appl. Artif. Intell..

[15]  Wen-Jye Shyr,et al.  Another sufficient condition for the stability of grey discrete-time systems , 2005, J. Frankl. Inst..

[16]  Naiming Xie,et al.  On the properties of small sample of GM(1,1) model , 2009 .

[17]  Qiang Ji,et al.  Forecasting China's natural gas demand based on optimised nonlinear grey models , 2017 .

[18]  P. Young.  Data-based mechanistic modelling and forecasting globally averaged surface temperature , 2017 .

[19]  Chun-I Chen,et al.  The necessary and sufficient condition for GM(1, 1) grey prediction model , 2013, Appl. Math. Comput..

[20]  Yong Wei,et al.  Discrete Verhulst model based on a linear time-varying , 2014, Grey Syst. Theory Appl..

[21]  Naiming Xie,et al.  Optimal solution for novel grey polynomial prediction model , 2018, Applied Mathematical Modelling.

[22]  Naiming Xie,et al.  Prediction Model of Interval Grey Number Based on DGM (1,1) , 2010 .

[23]  Wei Cui,et al.  Non-homogenous discrete grey model with fractional-order accumulation , 2014, Neural Computing and Applications.

[24]  Jin Xu,et al.  Improvement of grey models by least squares , 2011, Expert Syst. Appl..

[25]  Shuo-Pei Chen,et al.  Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM(1, 1) , 2008 .

[26]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[27]  Keith W. Hipel,et al.  An optimized NGBM(1,1) model for forecasting the qualified discharge rate of industrial wastewater in China , 2011 .

[28]  Xin Ma,et al.  Research on the novel recursive discrete multivariate grey prediction model and its applications , 2016 .

[29]  William Remus,et al.  Neural Network Models for Time Series Forecasts , 1996 .

[30]  Mark Evans,et al.  An alternative approach to estimating the parameters of a generalised Grey Verhulst model: An application to steel intensity of use in the UK , 2014, Expert Syst. Appl..

[31]  Jing Zhao,et al.  Using a Grey model optimized by Differential Evolution algorithm to forecast the per capita annual net income of rural households in China , 2012 .