The development of discriminants to prevent erroneous prediction by GM(1, 1)

Abstract

Owing to computer floating-point errors, a singular phenomenon is observed in GM(1, 1) (first order one variable grey differential equation model) when the grey development coefficient equals zero, causing fatal and meaningless prediction errors in following calculations. To prevent such a phenomenon from leading to an erroneous prediction result, discriminants for judgment should be developed. In this study, the method of symbolic operations is adopted to develop the general discriminants. Two discriminants, which are used for even and odd numbers of raw data, respectively, are successfully developed to play an important role in validating the feasibility of GM(1, 1). Two practical examples are used to demonstrate the importance of discriminants.

Keywords:

• Grey prediction
• singular phenomenon
• symbolic operation
• discriminants