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

Huiming Duan,Kailiang Shao,Xinping Xiao,Jinwei Yang

doi:10.1155/2017/9728587

Abstract

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 NDGMp/q) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of NDGMp/q and the NDGMp/q can decrease the disturbance bound. Subsequently, the parameter estimation method of NDGMp/q was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of NDGMp/q and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of NDGMp/q was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model.

Highlights

Forecasting the future values of time series data plays a very important role in our research; many forecasting methods have been developed for many years, such as the Rough sets theory proposed by Pawlak and fuzzy mathematics proposed by Zadeh
The results indicate there is no error between original value and simulative value based on pure nonhomogeneous index sequence
From the perspective of model stability, NDGM푝/푞 model is more stable than traditional nonhomogeneous discrete grey model (NDGM), and it was the result of a case to explain the stability

Summary

Introduction

Forecasting the future values of time series data plays a very important role in our research; many forecasting methods have been developed for many years, such as the Rough sets theory proposed by Pawlak (see [1, 2]) and fuzzy mathematics proposed by Zadeh (see [3]). According to improve simulation and prediction accuracies, there were some the results [22, 23] of Mathematical Problems in Engineering nonhomogeneous discrete grey model. These models had a higher requirement for data; when the data did not meet the requirements, the errors of both model-fitting and prediction were larger. The Particle Swarm Optimization algorithm was employed to optimize the order number of the NDGM푝/푞 model and obtained the better simulation and prediction results.

NDGM Model with Fractional Order Accumulating Operator

Conclusion