Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

The grey forecasting model has been successfully applied in numerous fields since it was proposed. The nonhomogeneous discrete grey model (NDGM) was approximately constructed based on the nonhomogeneous index trend; it increased the applicability of discrete grey model. However, the NDGM required accurate data and better effect when the original data did not meet the conditions and fitting and prediction errors were larger. For this, the NDGM with the fractional order accumulating operator (abbreviated as ) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of and the can decrease the disturbance bound. Subsequently, the parameter estimation method of was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model.