Fractional Order Accumulation NGM (1, 1, k) Model with Optimized Background Value and Its Application - Jun Zhang; Yanping Qin; Xinyu Zhang; Bing Wang; Dongxue Su; Huaqiong Duo (Journal of Mathematics)
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.