A novel unbiased multi-variable grey model

Purpose The multivariable grey model, a type of multi-output grey model, offers a unified representation of variables from a systemic perspective, carrying significant theoretical implications. However, traditional grey modeling methods generate errors, particularly the jump error from a difference equation to a differential equation. This paper aims to propose an unbiased multivariable grey model to eliminate these inherent errors. Design/methodology/approach This paper begins by analyzing the sources of errors in the multivariate grey model and subsequently optimizes its parameters to achieve an unbiased outcome. The properties of the unbiased multivariable model are discussed and mathematically proven. The model’s unbiased nature is further validated using data. Finally, the unbiased multivariable grey model is applied to two case studies. Findings Results indicate the unbiased model aligns completely with simulations and predictions of curves generated by the prediction formula of the multivariable grey model, eliminating its inherent bias. Numerical examples show that the proposed unbiased modeling method enhances the accuracy of the multivariable grey model. Originality/value A novel unbiased multivariable grey model is introduced, supported by rigorous mathematical proofs of its properties. Additionally, two case studies compare this model with GM(1,1) and four other multivariable grey models.