Fractional Order Accumulation NGM (1, 1, k) Model with Optimized Background Value and Its Application

Abstract

Aiming at the problem of unstable prediction accuracy of the classic NGM (1, 1, k) model, the modeling principle and parameter estimation method of this model are deeply analyzed in this study. Taking the minimum mean absolute percentage error as the objective function, the model is improved from the two perspectives of the construction method of the background value and the fractional order accumulation generation. The fractional order accumulation NGM (1, 1, k) model based on the optimal background value (short for the FBNGM (1, 1, k) model) is proposed in the study. The particle swarm optimization algorithm is used to estimate the parameters of the proposed model. Taking two actual cases with economic significance as examples, empirical analysis of the proposed model is conducted. The simulation and prediction results show the practicality and efficiency of the FBNGM (1, 1, k) model proposed in this study, which further broadens the application scope of the grey prediction model.

Prediction of WEEE Recycling in China Based on an Improved Grey Prediction Model

“…Wang and Li [47] developed a new grey Verhulst model combined with the PSO algorithm to predict CO 2 emissions in China. Zhang et al [48] proposed a fractional-order cumulative NGM (1,1,k) model based on optimal background values by optimizing the model parameters using the PSO algorithm. Hu [49] used a genetic algorithm to optimize the background value coefficients for a multivariate grey prediction model constructed for the bankruptcy prediction problem.…”

A New Grey Prediction IANGM (1,1, k, k2) Model

“…Due to the existence of different characteristics of data in real life, most of the models constructed by such methods cannot achieve better modeling results. Therefore, scholars have studied the optimization methods of the model from different angles and integrated the research methods: First, the improvement of the model, such as optimizing the grey derivative [9,10], the grey action [11][12][13], etc; the second is the improvement of the sequence generation method, such as reverse accumulation [14][15][16][17][18][19]and one-time accumulation [20,21]. These new optimization methods have achieved certain practical application results and further broadened the application scope of the grey model.…”

A novel grey prediction model with structure variability and real domain fractional order and its performance comparisons

“…Research on this class of optimization models has focused on the optimization of model performance parameters (initial value, background value and cumulative order) (Wang et al, 2018;Tong et al, 2022). Existing parameter optimization can be divided into single optimization of model parameters (Zeng et al, 2020c;Lu and Li, 2020) and combinatorial optimization (Zhang et al, 2020) according to the number of parameters to be optimized. In combinatorial optimization, according to the order of optimization, it can be divided into simultaneous optimization and stepwise optimization (Zhou et al, 2021;He et al, 2021).…”