On the Limitations of Univariate Grey Prediction Models: Findings and Failures

Abstract

Grey systems theory can be used to predict the evolution of a system with insufficient information. Unfortunately, the most used version of the grey model (GM), namely, GM(1,1), works best when the system series have an increasing exponential rate. In any other case, the GM(1,1) produces inaccurate predictions. In this paper, we examine the mathematical formulation of the conventional GM(1,1) in order to propose a new GM that addresses its shortcomings through a new time response function. Examples are presented to demonstrate the flexibility and accuracy of the new model when implemented with series of various natures. Comparisons with other intelligent GM(1,1) show that the proposed model performs better than the reference models.