A novel multivariate grey model for forecasting the sequence of ternary interval numbers

•New model is suitable for the sequence of ternary interval numbers through new parameter setting.•New model takes into account the influencing factors on the system behavior characteristic.•The accumulation method based on new information priority is proposed to estimate parameters.•Multivariate and univariate grey models are combined based on the degree of grey incidence. A novel multivariate grey model suitable for the sequence of ternary interval numbers is presented in the paper. New model takes into account the influencing factors on the system behavior characteristic. New parameter setting makes the model directly applicable to the sequence of ternary interval number without the need to convert the sequence into real sequence. A compensation coefficient taken as a ternary interval number is added to the model equation. The accumulation method based on the new information priority is proposed to estimate coefficients. A connotative prediction formula is derived to replace the white response equation of the classical multivariate grey model. The single variable grey model, which takes into account the development trend of system behavior itself, is combined with the novel multivariate grey model based on the degree of grey incidence. Interval forecasts for China's electricity generation and consumer price index show that the new model has good performance.