The grey opposite-direction model with fractional-order accumulation ($$ {\text{GOM}}^{\text{r}} (1,1) $$) has been appealed and interested in non-equidistant cases. However, there exists the drawback that it does not consider the effect of time-varying factor. In other words, the fixed grey control parameter defined as a certain constant limits the prediction performance of the model. By fully studying modelling procedure of the model, the optimized non-equidistant $$ {\text{GOM}}^{\text{r}} (1,1) $$ model with time-varying characteristics is proposed in this paper, which is abbreviated as $$...
