Study of the grey Verhulst model based on the weighted least square method

Analysis is conducted on the sources of several fitting errors of the grey Verhulst model, including approximation construction of the background value, inconsistency among the parameters of the difference and differential forms, the objective function setting of parameter estimation, and so on. However, constructing the precise background value of this model is complicated. A new parameter estimation method based on weighted least squares is proposed by transforming the model and using the approximate transformation of the objective function. Moreover, weights are determined by the converted form of target functions. In addition, the properties of the model under the new parameter form are studied. The proposed model avoids the process of precise background value construction as well as conversion from differential to difference equations. Empirical analysis shows that the method is effective. •This study analyses the main source of error in the traditional method.•We propose a new parameter estimation method based on the WLS method.•The new method is simpler than the traditional method in existing literatures.•The prediction accuracy of new method outperforms other three methods.